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Shrike

Shrike

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All users may post questions about MCAT and OAT physics here. We will answer the questions as soon as we reasonably can. If you would like to know what physics topics appear on the MCAT, you should check the MCAT Student Manual (http://www.aamc.org/students/mcat/studentmanual/start.htm), though be warned, there are subjects listed there that are rarely tested, or that appear in passages only and need not be learned.

Be sure to check the Physics FAQs and Topic Writeups thread if you have a general question; eventually, many of your answers will be located there. Also, a request: to keep this thread at least somewhat neat, when replying to someone else's post please refrain from quoting anything more than what's necessary for clarity.

Acceptable topics:

  • general, MCAT-level physics
  • particular MCAT-level physics problems, whether your own or from study material
  • what you need to know about physics for the MCAT
  • how best to approach to MCAT physics passages
  • how best to study MCAT physics
  • how best to tackle the MCAT physical sciences section
Unacceptable topics:

  • actual MCAT questions or passages, or close paraphrasings thereof
  • anything you know to be beyond the scope of the MCAT

Side note: anyone who knows how to post subscripts and superscripts in this system, please PM me the method. I also wouldn't mind knowing how to post some obvious symbols, such as Greek letters and an infinty sign. Should be a matter of changing fonts, but I don't know what's available; again, a PM would be appreciated.

If you really know your physics, I can use your help. If you are willing to help answer questions on this thread, please let me know. Here are the current official contributors to the this thread -- a team to which I hope to add more people:

Thread moderated by: Shrike. Shrike is a full-time instructor for The Princeton Review; he has taken the MCAT twice for no good reason, scoring 14 on the physical sciences section each time. He majored in mathematics, minored in physics, and spent several years accumulating unused school experience (in economics and law).

Also answering questions: Xanthines, a Kaplan instructor. He scored 13 on the PS section of the MCAT and 34 overall.
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So I'm reading my kaplan books (and others) and for example snell's law ( or any thing with a trig function) will come up and Ill derive it down (because after all I do have all equations memorized ) and I'll get something like Sin@=.3/1.8 (@=theta) and then the next thing I know the answer reads @=9.5 degrees. How do I do that? I believe its inverse sin, but in my head, come on?? Any help on how to figure problems like this out in a hurry would be great! Thanks!
 
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Futuredoctr said:
So I'm reading my kaplan books (and others) and for example snell's law ( or any thing with a trig function) will come up and Ill derive it down (because after all I do have all equations memorized ) and I'll get something like Sin@=.3/1.8 (@=theta) and then the next thing I know the answer reads @=9.5 degrees. How do I do that? I believe its inverse sin, but in my head, come on??
Click to expand...
Good question, but the answer may be unsatisfying: you don't have to be able to do this on actual MCAT questions. All you would need to be able to do, at the very most, on a problem like the one you quoted is to see that sin(theta) is (a lot) less than 0.5, the sin of 30 degrees, so the angle is also (a lot) less than 30 degrees. That'll be enough to choose the answer using process of elimination.

So, here's the general aproach to MCAT questions that ask for an angle as an answer. First, the only angles you need to know anything about are 30, 45, and 60 degrees (plus things like 0 and 90, plus equivalent angles like 135 [which is the same as 45]). Moreover, you don't need to know them with any precision: on MCAT physics questions, one significant figure is plenty. This means that for 30 degrees, sine is 0.5 and cosine is 0.9; for 60 degrees these two are reversed, and for 45 degrees the sine and cosine are each 0.7. (Warning: MCAT chemistry questions sometimes do require more than one significant figure, but there's no trig needed for them.)

How, then, do you answer questions whose answers are other than these? Glad you asked. The rule is this: angular answers to MCAT problems can only be angles you know about, plus angles that are actually discussed in the question or the passage, unless only one of the four answer choices is possible. In other words, any answer choice that is an angle that you don't know anything about (i.e., haven't memorized the sine and cosine of) and that isn't listed in the passage, cannot be the answer unless all other choices are obviously wrong.

For the problem listed, either they gave you an abbreviated trig table listing, among other angles, 9.5 degrees, or that was an angle that was discussed in the passage, say an initial angle or an experimental value, or all the other choices were 30 degrees or more (or 0). No, that probably wasn't the case in your practice material, but on the MCAT, it will be so.
 
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Next question if you have time. What equations are a must for the MCAT, as my review material contains seriously A LOT of equations, and if I need to commit them to the small memory I have left I should start now ;) .
 
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Futuredoctr said:
What equations are a must for the MCAT, as my review material contains seriously A LOT of equations, and if I need to commit them to the small memory I have left I should start now ;) .
Click to expand...
That one's going to take some time to put together; give it a while, please, but eventually I'll have it in the FAQs.

Re my editing of your second post: I'm just trying to keep the thread fairly uncluttered, so I took out the big quotation of my answer.

Thanks for moving your question in here, and congratulations on being the first to take advantage of the new forum. I appreciate the opportunity to help.

To others: I'll be looking for help. If you know your physics and want to lend a hand, please PM me.
 
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Hey Shrike, I can put together some equations if you want. I scored a 13 on the PS section a few years back. Just tell me if you are busy
 
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Hey Shrike,
I guess my question to you would be about how best to tackle Physics.....it's been a loooong time since I took physics, and I'm having a hard time trying to learn all this stuff again. I guess the stuff that's giving me the most trouble is Newtonian Mechanics, but I really do need to go over everything. So what would you suggest is the best way to tackle it? Thanks.
 
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DarkLordofSith said:
I guess my question to you would be about how best to tackle Physics.....it's been a loooong time since I took physics, and I'm having a hard time trying to learn all this stuff again. I guess the stuff that's giving me the most trouble is Newtonian Mechanics, but I really do need to go over everything. So what would you suggest is the best way to tackle it? Thanks.
Click to expand...
You will need to two things by the time you're done: (1) the basic equations, a list of which I'll be compiling (there are somwhere between thirty and fifty that I believe you absolutely must know) and some related definitions; and (2) an understanding of the major concepts. For example, with Newtonian mechanics, you need F = ma, F(G) = GMm/R^2, the equations for uniformly accelerated motion (e.g., d = v(0)t + 0.5at^2), and an understanding of three concepts: velocity and acceleration can be in the same or different directions; all forces and motion can be broken into x- and y-components, which you then deal with separately; and with projectiles, once you've broken the motion down into components the x-component is trivial, because v(x) remains constant always.

That's the general idea, though of course it doesn't really answer your question. Give me a while; I'll be writing it up. Essentially, I need to put nine two-and-a-half-hour lectures into print, and I don't type fast. Meanwhile, the more specific questions are easier to address, but keep asking whatever you want answers to.
 
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Thanks for the help......Just a suggestion, but could you do a thread that's "General Physics Concepts" and put it in there......this thread could be more for specific questions and the other one could be a thread exclusively for mods where you add general info that you feel would be beneficial for the average test taker to know.
 
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alright torque problem:
a massless plank with a length of 4 m has two weights placed on it. One with a mass of 10 kg on the left edge of the plank, while the other mass of 20 kg is placed 1.5 m inward from the opposite right edge. Where should the fulcrum be located if the plank with the weights on it were to remain horizontal?
Also do i have to use the CCW and CW to determine whats negative and positive torque?
 
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Abe said:
a massless plank with a length of 4 m has two weights placed on it. One with a mass of 10 kg on the left edge of the plank, while the other mass of 20 kg is placed 1.5 m inward from the opposite right edge. Where should the fulcrum be located if the plank with the weights on it were to remain horizontal?
Click to expand...
The plank is massless, so only the two weights matter. Never mind the equation for this problem; one's twice as heavy, so the fulcrum needs to be only half as far from it. With the numbers given, one third of the distance between the two weights is 0.83m from the larger mass, 1.67 from the smaller mass (and therefore the left edge).

When using the center of mass equation/center of gravity equation, I recommend always putting the zero at the left-most mass or force (because you're used to zero being on the left). If you do that, you don't have to mess with the signs so much when handling torques: up is one sign, down is the other; no clockwise or counterclockwise.

The center of mass (which is where you want the fulcrum) is at

CoM = (m1X1 + m2X2)/(m1 + m2) = (10kg x 0m + 20kg x 2.5m)/(20kg + 10kg) = (5/3)m = 1.67m​
 
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Abe said:
Also do i have to use the CCW and CW to determine whats negative and positive torque?
Click to expand...
Don't worry about using a different sign for different directions. In most problems, you care only about equilibrium, so everything zeros out anyway. If you have to calculate a torque, figure out its magnitude and then ask yourself what direction it's going.
 
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DarkLordofSith said:
Just a suggestion, but could you do a thread that's "General Physics Concepts" and put it in there......this thread could be more for specific questions and the other one could be a thread exclusively for mods where you add general info that you feel would be beneficial for the average test taker to know.
Click to expand...
We may eventually arrange it that way; we'll see what we come up with by way of general concepts (and how quickly).

Thanks for the suggestion.
 
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I could really use some help in understanding the buoyancy force in relation to figuring out the density of an submerged object. The archimedes principle.
 
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blankguy said:
Why is it that no current runs through a capacitor in a circuit if the circuit has been on for a while?
Click to expand...
Because that's the nature of a capacitor. The way a capacitor stores charge, and therefore energy, is by keeping charges crossing from one part (one plate, in the usual parallel plate capacitor) to the other, even though they want to. In the parallel plate capacitor, the plates are separated by a non-conductor, or by vacuum (which doesn't conduct current either). As long as the capacitor doesn't fail, charges can't cross through it.

The reason there is current in the short run is that charges are filling up the capacitor -- none of them is going through it.

When a capacitor fails -- it's often called dielectric breakdown -- the voltage has become high enough that those charges can get across the non-conductor (or vacuum) between the plates. Then, current flows, and all bets are off. This doesn't happen on the MCAT, as far as I know.
 
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blankguy said:
In the subject of machines(ramp, pulley, lever). Isn't the ramp inefficient in the way that the work(which leads to force) is being wasted on the horizontal component as opposed to lifting an object straight up in which everything goes to the vertical component?
Click to expand...
Not really. Pushing and pulling is conservative on the MCAT: no energy is lost. On the other hand, if energy is used to accelerate the block (up the ramp, or otherwise), then that energy isn't available to lift the block while the speed is increased (relative to its starting speed). On a complex problem this could matter, but in a simple problem we would assume either constant or negligible speed. In either of these simpler cases, all of the energy that goes into pushing or pulling is translated into potential energy by lifting the block, rather than kinetic energy by speeding it up.
 
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im confused with the topic if of weightlessness
a 5kg object is considered weightless when:
I chose when its accelarting up at 9.8 m/s^2
the answer is down, im just thinking weightless means mg is 0 so Forces acting on it should cancel out right? I dont know what im trying to say the answer and explanation they gave is confusing.
 
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Weight is the force due to gravity, which on earth is mg. An object has no weight when there is no acceleration due to gravity.

Alternatively, I guess an object could be considered weightless if something cancels out mg, like objects with densities identical to water that are submerged in water. This is why NASA conducts some of its training underwater and why senior citizens excercise in water. They don't have to deal with the forces being exerted by that pesky gravity.

Tell us what question/answer/explanation is giving you trouble and we can probably give a better response.

-X

Abe said:
im confused with the topic if of weightlessness...
Click to expand...
 
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thats what im saying if mg is pointing down and the answer i chose is the opposite of g than why isnt it weightless. Instead the answer is if it accelerates downward with g???
 
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Abe said:
im confused with the topic if of weightlessness
a 5kg object is considered weightless when:
Click to expand...
Weight is defined as the force of gravity on an object, and always equals mg. In popular parlance, an object is "weightless" when its apparent weight is zero. Apparent weight is just what a scale would read if the object were sitting on it; i.e., it's the force exterted on it, in an upward direction, by what it's resting on (or, occasionally, hanging from). An object is therefore weightless when the floor et al is not pushing it up; in other words, when it's in free fall.

Another example of apperent weight being zero is a neutrally buouyant object submerged in a fluid, or any object floating in equilibrium on the surface of the fluid. Because the buoyant force balances the force of gravity, no more force is needed to support it and a scale under the object would read zero.

Abe: if the object were accelerating upward at 10m/s^2, then that would be because there was a force pushing it up. That force would be sufficient to overcome gravity, and still push it upward just as fast as gravity wanted to push it down. Hence, its apparent weight would be doubled from what it was at rest -- the scale under it would read 2mg, because that's how strong the force would have to be.
 
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DarkLordofSith said:
Thanks for the help......Just a suggestion, but could you do a thread that's "General Physics Concepts" and put it in there......this thread could be more for specific questions and the other one could be a thread exclusively for mods where you add general info that you feel would be beneficial for the average test taker to know.
Click to expand...
Check out the new Physics FAQs and Topic Writeups thread; I'm pretty much following your suggestion to the letter. Thanks for the help.
 
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blankguy said:
I could really use some help in understanding the buoyancy force in relation to figuring out the density of an submerged object. The archimedes principle.
Click to expand...
Sorry; I've posted a fairly comprehensive answer to this somewhere, but now I can't find it. Be patient and I will get to it.
 
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for some reason, i cant figure out why a car is pushed away from the center of a circle when it goes around in a circle. the centripital force and i want to say that the static friction force are both facing into the middle (preventing the car from skidding away from the center)... so, i guess this should be some type of equilibrium situation. what force am i missing that pushes away from the center?
 
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Something happened when I first tried to post this, so I apologize if I left anything out.

The car is not being pushed away from the center of the circle. Without a centripetal force, objects such as cars and yo-yo's on strings will move in a direction that is tangential to the circular path.

In the case of your car making donuts in a level parking lot, the engine is providing the power for forward motion (by forward, I mean the front of the car). When you let go of the steering wheel, the car will move in a straight line that is tangential to the donuts you were making before.

You are correct in thinking the friction force points towards the center. That is because on level surfaces, the centripetal force is the friction force...

Fc = uFn = mv^2/r​

Without friction, there can be no circular motion for cars. This is what happens when you try to make turns on icy patches of the road. There is no friction to provide a centripetal force, and thus you skid off the road into a ditch.

Note: This is only for level surfaces. On banked highways and race tracks, gravity comes into play.

Also Note: There is no such thing as a "centrifugal force." This is the name commonly given to another physics term known as inertia.

-X

mrhealth said:
for some reason, i cant figure out why a car is pushed away from the center of a circle when it goes around in a circle. the centripital force and i want to say that the static friction force are both facing into the middle (preventing the car from skidding away from the center)... so, i guess this should be some type of equilibrium situation. what force am i missing that pushes away from the center?
Click to expand...
 
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thanks for the quick reply. so when what force is greater than the inward static frictional force does the car start skidding away?
 
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xanthines said:
There is no such thing as a "centrifugal force." This is the name commonly given to another physics term known as inertia.
Click to expand...
This part is not exactly true. You're right that by "centrifugal force," non-physicists usually mean something else: either inertia, or centripetal force. But there is such a thing as centrifugal force:

Recall that, by Newton's Third Law, for every force there's an equal and opposite force, and that the two constitute an action-reaction pair. Centrifugal force is the force that forms a pair with the centripetal force -- it's the force exerted by the body that's moving in a circle, on whatever's making it turn.

For example, in the case of a yo-yo whirled on a string, the force of the string on the yoyo is centripetal, and the force of the yo-yo on the strong, and thus your finger, is centrifugal. In the case of the car driving in a circle, the ground exerts a centripetal foce on the tires, while the tires exert a centrifugal force on the ground.

You might guess from these examples that it's centripetal force that we usually worry about, not centrifugal. You'd be right. Centrifigal force tends to be a little odd, and mostly irrelevant. I've never seen it matter on an MCAT problem.
 
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Sorry, I meant to say something like the Centripetal force isn't really a new type of force, but just the name used to indicate the force pointing inwards. In this case, it is the static frction force.

Since the static coefficient of friction is normally given as the maximum, you know that any more force applied to that object will overcome friction and will begin to slide or in the case of the car, skid off the road.

The centripetal force equation Fc=(m)(v^2)/r describes the force required to keep the object in a circular path. When the car moves fast enough, the force due to static friction will not be high enough to maintain circular motion. Incidentally, I've heard the term "centripetal force requirement" to describe the situation.

Likewise when a satellite or any other thing moves fast enough it will escape the earth's gravity:

G(Mearth)(Msatellite)/(r^2) is less than (msatellite)(v^2)/r

Again, I apologize for the incompleteness of my answer. Hope that helps!

-X

mrhealth said:
thanks for the quick reply. so when what force is greater than the inward static frictional force does the car start skidding away?
Click to expand...
 
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Shrike is right. I meant to say "There is no such thing as centrifugal force acting on you in the car...."

That is still inertia "pushing" you up against the side of the car. Centrifugal force is indeed the force the car exerts on the road.

Mea culpa.

-X
 
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thats why this is confusing to me. i dont know if this is beyond the scope of the MCAT or what. so if you draw a free body diagram (ignore the centrifugal force of the car on the ground because the car is the object, not the ground) with a car moving in a circle at constant velocity, then the only one force vector would be inward (=friction=centripital force), right? im sure this has to do with the velocity because intuitively i know that at a higher velocity, it would be harder for a car to stay in its circle. this is more out of curiousity now more than worrying that something like this will be on the mcat. thanks again for all your help.
 
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Pretty much!

The freebody diagram should show mg pointing downwards, the Normal Force (Fn) going up, and the Friction force (Ff) going towards the center of the circle. The centripetal force (Fc) is the force required to keep the car in a circular path at that velocity. Your intuition is correct. The fast you go, the higher the Fc. When the required Fc surpasses the Frictional force, the car begins to skid and circular motion is no longer maintained. When this happens, you'd better be wearing your seatbelt!

-X
 
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mrhealth said:
... with a car moving in a circle at constant velocity...
Click to expand...
A minor point, but just in case: the car may be moving at constant speed, but its velocity is changing because the direction is changing.
 
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All these threads will be up at least until August, right?
I know it is a dumb question, but I am debating about whether or not I should retake the exam.
This study area is great!
 
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Shrike said:
A minor point, but just in case: the car may be moving at constant speed, but its velocity is changing because the direction is changing.
Click to expand...


Hard to picture that because in real life we'd have to slow down to change directions(ie turn) while driving the car. An object that is being swung in a ciscular motion at constant speed would be easier to picture. Speed constand but the direction is changing.
 
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blankguy said:
Hard to picture that because in real life we'd have to slow down to change directions(ie turn) while driving the car.
Click to expand...
You apparently haven't driven with me.
 
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blankguy said:
I could really use some help in understanding the buoyancy force in relation to figuring out the density of an submerged object. The archimedes principle.
Click to expand...
Look here, and tell me whether it answers your question.
 
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riceman04 said:
All these threads will be up at least until August, right?
I know it is a dumb question, but I am debating about whether or not I should retake the exam.
This study area is great!
Click to expand...

They will be up permanently, as far as we know. I'm glad that you are finding them helpful. Best of luck for those taking the test in Aug. :luck:
 
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TPR asks in one of its hw problems the following:

In a series of experimental trials, a projectile is launched with a fixed speed, but with various angles of elevation. As the angle is increased from 0 to 90, the vertical component of the velocity:

Now, I picked the option that said: increases, while the horizontal component remains constant.

The answer, accodring to TPR is: increases, while the horizontal component decreases.

I thought horizontal velocity was constant during the duration of the flight.
 
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For some reason, I have a lot of trouble with some of the more basic physics subjects i.e. kinematics, Newtonian mechanics, conservation of energy, etc. I don't have an intuitive understaning of these topics and on MCAT problems that are more conceptual, I often waste a lot of time trying to overanalyze them and often end up picking the wrong answer. I'm not sure what do do about it, because I understand the basic concepts and know the formulas but I just can't seem to do well on the more conceptual problems -- an example would be how changing the angle of inclination would affect velocity, acceleration, etc. Basically problems that are really easy if you have an intuitive understanding of the concepts and how they are interrelated but extremely difficult if you do not.

I'd appreciate any advice on how I can improve on this. Thanks.
 
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Horizontal velocity IS contant during the duration of a flight (assuming no air resistance), but it is only constant with regard to your starting angle of elevation. Put another way, going from 0 to 90 degrees in one degree increments, will give you 90 different horizontal velocities, but they will be constant, ie they won't slow down or speed up.

As for your specific problem. Descriptively, at zero degrees all of the energy from the cannon will be directed in the horizontal component, making the projectile travel in a straight line parallel to the ground. Whereas at 90 degrees all of the energy will go into the vertical component, making the projectile travel straight up. The horizontal velocity would HAVE to decrease since you know that firing anything straight up into the air will come straight back down again. It won't move left or right. At 45 degrees both components will have equal values. This is why 45 degrees give you the best distance in the presence of gravity and the absence of aire resistance.

Remember that sin and cos of theta (ie angle of elevation) will tell you how much of the total starting velocity is composed of its horizontal and verical components. Just give an arbitrary starting velocity of 10 m/s and compare the sin and cos values as go from 0 to 90 degrees in 15 degree increments.

Example:
Vertical Component --> 10 m/s * sin(0) = 0 m/s
Horizontal Component --> 10 m/s * cos(0) = 10 m/s

Shrike is a TPR teacher. Perhaps he can comment better since he will probably know the HW Question you are talking about.

-X

Kussemek said:
TPR asks in one of its hw problems the following:

In a series of experimental trials, a projectile is launched with a fixed speed, but with various angles of elevation. As the angle is increased from 0 to 90, the vertical component of the velocity:

Now, I picked the option that said: increases, while the horizontal component remains constant.

The answer, accodring to TPR is: increases, while the horizontal component decreases.

I thought horizontal velocity was constant during the duration of the flight.
Click to expand...
 
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Which of the follwing gives the percent change to the Young's Modulus for a substance when its cross sectional are is increased by a factor of 3?

0
33%
300%
900%

I put 33% since the equation is F/A/ (Delta L/L)

But of course it was wrong and the answer was 0.

Also for another stress q:
The sole of a certain tennis shoe has a shear modulus of 4x 10 to the 7th, I f the height of the sole is double the strain will.

Decrease by factor of 2
Same
Increase by f of 2
Increase by f of 4

I put increase by f of 2 since, which is wrong, but is it 0 because young's modulus is height, and shear is length? Thanks
__________________
 
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xanthines said:
Shrike is a TPR teacher. Perhaps he can comment better since he will probably know the HW Question you are talking about.
Click to expand...
Naah. We don't look at homework problems until someone asks about them, and then we usually promptly forget the problem -- it's just not a big part of our class.

Xanthine's explanation is fine. For a given set of launch conditions, vx remains constant, but you're changing launch conditions.
 
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TheGuy2000 said:
Which of the follwing gives the percent change to the Young's Modulus for a substance when its cross sectional are is increased by a factor of 3?
Click to expand...
Young's modulus is a property of the material, like coefficient of friction or index of refraction. It doesn't change just because there's more stuff.

The equation is then used, with this fixed value, to figure the strain for a given stress.
 
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safeflower said:
...I don't have an intuitive understaning of these topics and on MCAT problems that are more conceptual, I often waste a lot of time trying to overanalyze them and often end up picking the wrong answer. I'm not sure what do do about it.
Click to expand...
Tough problem. Some solutions ideas:

  • Move to Dallas, and take my class.
  • Arrange to get better instruction at your school.
  • Keep an eye on the FAQs and Topic Writeups thread, where I'll be trying to give ways to deal with conceptual problems.
  • Find a self-study source that promotes conceptual understanding. I'm told Examkracker's physics text is good for this, but I can't tell you from firsthand knowledge. As an extreme solution, you could get a book of the Feinman lectures.
 
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Well, a less ideal way would be to just memorize what happens if you do X. Since you already know the euquations and concepts, you could memorize a few key "happenings" despite the lack of intuition. Again, it would be better if you could "just get it", but in the absence of that (or Shrike's suggestions) this may help you through the physics Q's.

-X

safeflower said:
For some reason, I have a lot of trouble with some of the more basic physics subjects i.e. kinematics, Newtonian mechanics, conservation of energy, etc. I don't have an intuitive understaning of these topics and on MCAT problems that are more conceptual, I often waste a lot of time trying to overanalyze them and often end up picking the wrong answer. I'm not sure what do do about it, because I understand the basic concepts and know the formulas but I just can't seem to do well on the more conceptual problems -- an example would be how changing the angle of inclination would affect velocity, acceleration, etc. Basically problems that are really easy if you have an intuitive understanding of the concepts and how they are interrelated but extremely difficult if you do not.

I'd appreciate any advice on how I can improve on this. Thanks.
Click to expand...
 
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Yes, torque is covered. And it is listed on the MCAT topic list, as is rotational equilibrium, which requires an understanding of torque.
 
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Does anyone one know tricks to figuring out tangent, sine, and cosines in your head?
 
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Jezzielin said:
Does anyone one know tricks to figuring out tangent, sine, and cosines in your head?
Click to expand...
I don't know when you'd need tangent on the MCAT. Sine and cosine, you need only for a few angles:

  • sin(30) = 0.5; cos(30) = 0.9
  • sin(45) = 0.7; cos(45) = 0.7
  • sin(60) = 0.9; cos(60) = 0.5
Any other angle, you will be given the trig functions for, or you will only have to see that the function is bigger/smaller than one of the angles listed above.

The mnemonic for trig functions is SOH CAH TOA: sine = opposite over hypotenuse, cosine = adjacent over hypotenuse, tangent = opposite over adjacent.

In the future, please ask your questions in this thread, rather than starting a new thread. Thanks.
 
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