Solving $\cos(x/2) = \sin x$

Question

Can anyone give me just a hint as to how to go about solving this? Yes it is for homework, but I don't want an answer, just a bit of guidance. I'm thinking the half angle formula for the first bit, but it doesn't seem to look right.

$$\cos(x/2)-\sin(x) = 0$$

Thanks!

score 5 · Accepted Answer · answered Jul 19 '11 at 00:20

5

Let $y=\frac{x}{2}$, so that your equation is $$\cos(y)=\sin(2y).$$ Do you know any formulas that you can use here?

answered Jul 19 '11 at 00:20

Zev Chonoles

129,973

Thanks! That was just what I needed to get the brain started :) – Josh Jul 19 '11 at 00:32
No problem, glad I could help :) – Zev Chonoles Jul 19 '11 at 00:33

score 2 · Answer 2 · answered Jul 19 '11 at 00:30

2

You could also try rewriting $\sin x$ as $$\sin x =2\sin \frac{x}{2}\cos\frac{x}{2}.$$

answered Jul 19 '11 at 00:30

Nana

8,351

Solving $\cos(x/2) = \sin x$

2 Answers2