Hi
quick & easy question:
6 cos 4x = 6 sin 8x
cos 4x = sin 8x
cos 4x = 2 sin 4x cos 4x
1/2 = sin 4x
arcsin(1/2) = 4x
x = arcsin(1/2)/4
are the above steps correct?
If so, how can i find x in terms of pi?
Thanks.
Not quite. Dividing through by $\displaystyle \cos(4x)$ is potentially dividing by 0 so instead move all terms onto one side and factor
$\displaystyle 2\sin(4x)\cos(4x) - \cos(4x) = \cos(4x)(2\sin(4x)-1) = 0$
Either $\displaystyle \cos(4x) = 0$ (these are the solutions you miss if you divide) or $\displaystyle 2\sin(4x)-1 = 0$
As for $\displaystyle \arcsin(0.5)$ recall your unit circle to see that $\displaystyle \arcsin(0.5) = \dfrac{\pi}{6}$