1. intersection of graphs

I need to find the points of intersection of sin 2x and sin 4x in degrees. I can do this kind of question but this one is difficult.

2. Originally Posted by Stuck Man
I need to find the points of intersection of sin 2x and sin 4x in degrees. I can do this kind of question but this one is difficult.
Use the identities for sin(4x) and sin(2x)

$\displaystyle \sin(4x) = 4\sin(x) \cos^3(x) - 4\sin^3(x) \cos(x) = 4\sin(x) \cos(x)(\cos^2(x)-\sin^2(x))$

$\displaystyle \sin(2x) = 2 \sin(x) \cos(x)$

$\displaystyle 4\sin(x) \cos(x)(\cos^2(x)-\sin^2(x)) = 2 \sin(x) \cos(x)$

$\displaystyle 4\sin(x) \cos(x)(\cos^2(x)-\sin^2(x)) - 2 \sin(x) \cos(x) = 0$

$\displaystyle [2 \sin(x) \cos(x)][2cos(2x)+1] = 0$

Either $\displaystyle \sin(x) = 0$, $\displaystyle \cos(x) = 0$ or $\displaystyle 2\cos(2x)+1 = 0$

3. Identities of sin 4x aren't part of my course so I should be using the ones usually learned earlier. I can use sin 2x and cos 2x.

4. I have done it using sin 4x = sin(2x + 2x). It was particularly hard compared to previous questions in the book.