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Sine,Cos,Tan!

Hi so I'm a little stuck a question to do with sine, cos and tan.

So the question goes like this:

If sin x = a and cos x = b:

Find (in terms of a and b):

1. cos(270+x)

2. -2 tan (-x)

3. 2 cos^2(180+x)



I've had a go at them but I'm finding it quite confusing so it would be good if you could explain how you did it as well as stating your answer.
Thanks!
Reply 1
Avatar for Jack_8
Jack_8
OP
Anyone? :smile:
Reply 2
Avatar for Kolya
Kolya
17
Original post by Jack_8

Original post by Jack_8
Anyone? :smile:


For the first one: do you remember the formula to expand cos(x+y)cos(x+y)?
For the second one: can you write sin(−x)sin(-x) and cos(−x)cos(-x) in terms of sin⁡(x)\sin (x) and cos⁡(x)\cos (x) respectively?
Reply 3
Avatar for Jack_8
Jack_8
OP
I'm not totally sure what you mean by the formula to expand that...

and for the second one, wouldn't sin(-x) just be -sin(x) ?
Reply 4
Avatar for Kolya
Kolya
17
Original post by Jack_8

Original post by Jack_8
I'm not totally sure what you mean by the formula to expand that...

and for the second one, wouldn't sin(-x) just be -sin(x) ?


Yes for the second one.

For the first one, you should have seen a formula which is something like cos⁡(A+B)=cos⁡Acos⁡B−sin⁡Asin⁡B\cos (A+B) = \cos A \cos B - \sin A \sin B. You need to apply that. (nb. i'm not confident about my recall of that formula - it's been a long time since i've used it! - so you should look it up to check.)
Reply 5
Avatar for eswnl
eswnl
For the first one, use Cos(A+B)=cosAcosB-SinASinB
For the second, I used Tanx = Sinx / Cosx.
For the 3rd one, you can use the formula from the first question,

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