Determining Quadrants and Values of sin/cos/tan etc followed by degrees?

[Member 8586]

Probably a simple answer/stupid question, but Im completely unfamiliar with Trig and just learning as Im going along by following the common formulas I see.....I've just memorized the unit circle too, but havent found a question I can use it on? (esp the fractional values; radians can easily be figured out)....I think Quadrant 1 = (+cos, +sin), Q2 = (-cos,+sin), Q3 = (-cos,-sin), Q4 = (+cos,-sin)? Is that right? What about tan, sec, cot, csc??

but as for a questions like

Which of the following is not true?
a) sin 295 < 0
b) sec 295 > 0
c) tan 295 < 0
d) cos 295 < 0
e) csc 295 <0

I have no idea how to go about this...? What's what in what quadrant?

Cos (116*) = ?

^Another [I think similar] example I was clueless about

and different from the others:
(2011 Destroyer #146) If f(x) = tan x + cot x and g(x) = csc x, then which of the following is equal to f(x)/g(x)?
sin x, cos x, tan x, sec x, or csc x?


Feel free to help with one, two or all lol...any help is appreciated! Thanks!

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[Dgeorg6]

tan = sin/cos

cot = cos/sin

sec = 1/cos

csc = 1/sin

so d is not true because 295 is in the 3rd quadrant and as you have already written, cos is + in the 3rd quadrant meaning it is >0 not <0

your 2nd question I would assume you would just type into your calculator?

3rd question is more trig identities. I think it would factor to 2sincos which = something, but im not sure..

It would be something like ((sin/cos) + (cos/sin))/(1/sin) and then factor

 

[Member 8586]

Chad to the rescue! well somewhat lol...ok so for the following problem, I get the sin and cos functions, but the others is what im unsure about

Which of the following is not true?
a) sin 295 < 0
b) sec 295 > 0
c) tan 295 < 0
d) cos 295 < 0
e) csc 295 < 0

a) sin negative in IV OK
d) cos positive in IV - OK so that's why this is the answer

as for b,c,e:
b) sec = 1/cos so 1/positive = positive?
c) tan = sin/cos so negative/positive = negative?
e) csc = 1/sin so 1/negative = negative?


For Cos (116*) = OK I see why - Only sin is positive in the second quadrant, so sin 64 will be equivalent to the cos 116 (probably need to see the answer choices as I'm thinking there's multiple possibilities?)

Any help on the last problem?

 

[Member 8586]

bump 🙁

 

[KyoPhan]

tan = sin/cos
so d is not true because 295 is in the 3rd quadrant and as you have already written, cos is + in the 3rd quadrant meaning it is >0 not <0

4th quadrant isn't it?

In high school, I remembered this by ASTC - All Students Take Calculus. Starting from the top right quadrant, and working counter clockwise. A=all, S=sin T=tan C=cos. Here's a picture.
http://media.wiley.com/Lux/49/184749.image0.jpg


If your doing this by finding the equivalent, it is a waste of time. Your thinking too hard.

Since your only dealing with 295 degree, you just need to realize it ends up in the 4th quadrant. In the 4th quadrant, cos are all positive, and thus sec is also positive since sec=1/cos.

d)cos 295<0 is saying that's a negative, but it should be positive from what I just said

Chad to the rescue! well somewhat lol...ok so
as for b,c,e:
b) sec = 1/cos so 1/positive = positive?
c) tan = sin/cos so negative/positive = negative?
e) csc = 1/sin so 1/negative = negative?

For Cos 116, it lies in 2nd quad, where sin/csc are positive. So cos 116 is negative. That's how simple it is.

 

[Member 8586]

4th quadrant isn't it?

In high school, I remembered this by ASTC - All Students Take Calculus. Starting from the top right quadrant, and working counter clockwise. A=all, S=sin T=tan C=cos. Here's a picture.
http://media.wiley.com/Lux/49/184749.image0.jpg


If your doing this by finding the equivalent, it is a waste of time. Your thinking too hard.

Since your only dealing with 295 degree, you just need to realize it ends up in the 4th quadrant. In the 4th quadrant, cos are all positive, and thus sec is also positive since sec=1/cos.

d)cos 295<0 is saying that's a negative, but it should be positive from what I just said

For Cos 116, it lies in 2nd quad, where sin/csc are positive. So cos 116 is negative.

thanks!..so basically what i said here was correct, rite?
as for b,c,e:
b) sec = 1/cos so 1/positive = positive?
c) tan = sin/cos so negative/positive = negative?
e) csc = 1/sin so 1/negative = negative?

any idea about the solution to the last question i posted in the original post?

 

[KyoPhan]

Yes! That's correct; however, in regards to c. What you said is correct, but it would be wise to just instantly think that it's negative, since it is not the reciprical of sin. It'll save you some time in my opinion.