Question

Can someone help?

Rewrite with only sin x and cos x.

cos 2x + sin x

Answer 1

There is a formula that states that cos(2x)=cos^2(x)-sin^2(x) try to use it.
Those formulas are not necessary to remember if you have a basic understanding of imaginary or complex numbers and if you do I can show you, but if you don't I strongly advise you to try to memorize them.

Answer 2

Thanks. So then I get cos^2 x - sin^2 x + sin x? And I have a very very very basic understanding of imaginary/complex numbers. I highly doubt enough to really help shortcut any process. Trig is not quite my thing. So once I get the new identities, what do I do next?

Answer 3

Well, thats the end of your problem. I think you might be able to understand the complex thing.
You wont understand the equation but that will be the only one you'll have to remember:
\[e^{i \theta}=\cos \theta+i \sin \theta\]
What you need to do when you are trying to remember a trig formula is put the angle in the first part and see what you got. I'll do it for the formula we used on this problem.
We want cos(2x), so we want only the real part (without the i) of the formula above.
\[e^{i2x}=e^{ix}e^{ix}\]Now we just need to write those two in sin and cos form.\[e^{i2x}=\cos(2x)+i \sin(2x)\]Taking the real part we get cos(2x).
\[e^{ix}e^{ix}=(\cos x+i \sin x)(\cos x+i \sin x)=\cos^2 x-\sin^2 x+i2\cos x \sin x\]The minus appears because i^2=-1 because i is the sqrt(-1)
Taking only the real part we get cos^2+sin^2 and making them equal we get the identity we used.
If you use the imaginary part instead, we get the equation for sin(2x)=2cos(x)sin(x)

Answer 4

This can help you a lot if you understand it, but if you don't just forget it because it might confuse you.

Answer 5

So, did you get the complex thing?