how do you do arctan by hand?

[shaq786]

here is a specific problem... tan (theta)= (50/30)

So that would be thetha = arctan(50/30)

The answer is theta equals 59 degrees

but how would you have been able to calculate that by hand? or would they just give you the answer that arctan(50/30) is 59 degrees?

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[Twitch]

I'm as calculator dependent as the next guy, so here is a fairly rough way to do it (assuming you've memorized the basic angles 0, 30, 45, 60, 90).

50/30 or 5/3 is more than 1 but less than 2. Since 3*2 = 6. So it's closer to 2 lets say somewhere between 1.5-1.75 or so.


now tan(theta) = 1.5-1.75.

Think back to the table I mentioned above. tan (60) = root under of 3.
What's root under of 3? Somewhere around 1.5-1.75 right? Close enough. Ideally you should also remember the decimal equivalents of the table above.

 

[Scubadoc]

i've had this same question.

i am still confused though!! 😕

 

[DieselPetrolGrl]

why would u ever want to do this?

 

[Scubadoc]

we had several questions like this in the kaplan PS books....you had to find the arctan to get the angle which gave you the direction of travel. really irritating! 😡

 

[Twitch]

Alternative explanation:

Here is the table of the basic angles:

0.0000 = sin(0 ?) 1.0000 = cos(0 ?) 0.0000 = tan(0 ?)
0.5000 = sin(30 ?) 0.8660 = cos(30 ?) 0.5773 = tan(30 ?)
0.7071 = sin(45 ?) 0.7071 = cos(45 ?) 1.000 = tan(45 ?)
0.8660 = sin(60 ?) 0.5000 = cos(60 ?) 1.7320 = tan(60 ?)
1.0000 = sin(90 ?) 0.0000 = cos(90 ?) +infinity = tan(90 ?)

You're looking for some theta such that you get the final answer to be 50/30 (or 5/3 or slightly less than 2 right since if it was 6/3 you'd get 2 so you're looking for slightly less than 2). Here are your choices distilled down:

(a) tan 0 = 0 (no way right, since you're looking for slightly less than 2)
(b) tan 30 = 0.58 (probably not, too far away from 2)
(c) tan 45 = 1 (probably not, still fairly far away from 2)
(d) tan 60 = 1.73 (fairly close to 2 but less than 2 - pretty close)
(e) tan 90 = inf (uhmm...no).

clearly the right answer is close to (d) or close to tan 60 degrees. As the OP points out it's exactly tan 59 but this method above gets you fairly close without a calc. The downside is you need to know the table above.

 

[liverotcod]

For MCAT purposes, I would draw a right triangle with segments approximately 5 and 3 cm. Then I would draw in the hypotenuse and guesstimate the angle formed with the x axis. Close enough!

 

[shaq786]

I'm as calculator dependent as the next guy, so here is a fairly rough way to do it (assuming you've memorized the basic angles 0, 30, 45, 60, 90).

50/30 or 5/3 is more than 1 but less than 2. Since 3*2 = 6. So it's closer to 2 lets say somewhere between 1.5-1.75 or so.


now tan(theta) = 1.5-1.75.

Think back to the table I mentioned above. tan (60) = root under of 3.
What's root under of 3? Somewhere around 1.5-1.75 right? Close enough. Ideally you should also remember the decimal equivalents of the table above.

That really sucks, so u might have to end up remembering root 3...root 3 divided by 2...1/root 3

all those decimels for arctan lol

Its like in some passages they'll give you the decimels and in some they dont

 

[Twitch]

That really sucks, so u might have to end up remembering root 3...root 3 divided by 2...1/root 3

all those decimels for arctan lol

Its like in some passages they'll give you the decimels and in some they dont

It's not that bad. If you're uncomfortable with the #'s you can always use the method liverotcod mentions and TPR also brings this point up if I remember from my SAT prep way back.

Think of it this way the middle column of the table (the cosine) column is just the reverse of the first column. The tangent column is fairly straight forward except for 1-2 #'s. So you really just need to know a handful of #'s (decimals/fractional form). You can do it.

Good Luck,
-Y_Marker