sine/cosine functions

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xc630

Junior Member
Joined
Sep 1, 2005
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164
Hi I'm having some trouble with these two problems. I would appreciate any help.

The first question asks name each quadrant described.

a) sin theta<0 and cos theta>0
I think this is Quad IV

b) sin theta>0 and sin (90 degrees + theta)>0.
I have no idea what this means.

The seocnd problem says solve each equation for all theta in radians without a calculator or table.

a) cos theta= 1
b) sin theta= -1
c) cos theta = 0
d) cos theta =-3
i have no idea how to do these either.

Thanks for your help
 
A) You have A correct. Do you know why this is?

B) What they are asking for here is for you to find the quadrant in which sintheta>0 and sin theta PLUS 90 degrees>0. In radians, this means sin theta plus pi/2. Just find the quadrant.

C) For these, remember that sin is y/r and cos is x/r. If you know your different points on a unit circle, this should be no trouble at all.
 
Can you give me example of how to do one? For 8a) costheta=1. This would mean the x=1 and y= 0 but how do you find r for cos=x/r?
 
a) correct

b) I think you know that if sinӨ>0, then it is either quad 1 or 2. Think about this, if sinӨ>0, then 0<Ө<180. So if sin(90+Ө)>0, then 0<90+Ө<180, or -90<Ө<90. This is either quad 1 or 4.
 
Radius of an unit circle is 1. That is why cosӨ=x and sinӨ=y. Btw, d) isn't possible because -1≤cosӨ≤1
 
I would just like to check my asnwers to make sure i am getting this right.

So a) costheta =1
would be 0

b) sin theta = -1
would be -pie/2 + 2npie where n is an integer

c) cos theta= 0
would be pie/2 + (-pie/2 + 2npie)

d) cos theta=-3
would be not possible
 
Pi is the number; pie is something you eat.

You can answer a) the same way you answered all the other questions. 0 radians is one answer but in general, the answer is 2(pi)(n) where n is an integer.

b) looks correct.

I'm not sure what your intended answer is on c). I think it should be pi/2+pi(n) where n is an integer.
 
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