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.

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- Mar 4th 2011, 03:41 PMKumaFinding trig intersection point
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. - Mar 4th 2011, 03:53 PMe^(i*pi)
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 $\displaystyle \arcsin(0.5) = \dfrac{\pi}{6}$