1. ## Expressions involving trigonometry

I did a past paper which had the following question:

Let p = sin40 and q = cos110. Give your answers to the following in terms of p and/or q.

Write down an expression for
(i) sin140

(ii) cos70.

Apparently the answer for (i) is p = sin140 and for (ii) cos70 = -q

I do not understand why is that the answer. Is it anything to do with the CAST unit circle idea? If it is then it would not make sense for cos.

Thanks

2. (i) Use the fact that you know that sin(v)=sin(180-v)
(ii) Use the fact that you know that -cos(v)=cos(180-v)

When you're facing problems involving angles that you "haven't seen" earlier in the problem, the solution often has something to do with the trig. identities! keep it in mind and learn how to derive them from the unit circle (the basic onces)!

3. Originally Posted by CSG18
Is it anything to do with the CAST unit circle idea? If it is then it would not make sense for cos.
Yes it does, good work.

$\cos (180- \theta) = -\cos\theta$

Think about this $q = \cos 110 = \cos (180 - 70) = -\cos 70$

I understand it now, but just to confirm, the reason why there is a minus sign in: -Cos(x) = cos(180-x) is because in the unit circle cos is only positive between 0 to 90 degrees and 270 to 360 degrees (I am aware it goes on).

What would be the equation for tan(x)?

Would it be -tan(x) = tan(180-x) ???

5. Originally Posted by CSG18

Would it be -tan(x) = tan(180-x) ???
Sounds good to me.