intersection of graphs

**Stuck Man** · February 4th 2010, 08:42 AM

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.

**e^(i*pi)** · February 4th 2010, 08:56 AM

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)

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

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

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

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

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

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

**Stuck Man** · February 4th 2010, 09:16 AM

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.

**Stuck Man** · February 4th 2010, 11:12 AM

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

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