# Math Help - Simple sinx...

1. ## Simple sinx...

sin(5x) / sin(x) = ? ...if I know that sin(3x) / sin(x) = 6 / 5

2. Hi

$\sin^3 x = -\frac{1}{4}\:\sin 3x + \frac{3}{4} \:\sin x$

Therefore
$\sin^2 x = -\frac{1}{4}\:\frac{\sin 3x}{\sin x} + \frac{3}{4} = -\frac{1}{4}\:\frac{6}{5} + \frac{3}{4} = \frac{9}{20}$

Now
$\sin^5 x = \frac{1}{16}\:\sin 5x - \frac{5}{16} \:\sin 3x + \frac{5}{8} \:\sin x$

Therefore
$\sin^4 x = \frac{1}{16}\:\frac{\sin 5x}{\sin x} - \frac{5}{16} \:\frac{\sin 3x}{\sin x} + \frac{5}{8}$

$\left(\frac{9}{20}\right)^2 = \frac{1}{16}\:\frac{\sin 5x}{\sin x} - \frac{5}{16} \:\frac{6}{5} + \frac{5}{8}$

$\frac{1}{16}\:\frac{\sin 5x}{\sin x} = -\left(\frac{9}{20}\right)^2 - \frac{5}{16} \:\frac{6}{5} + \frac{5}{8} = -\frac{19}{400}$

Finally
$\frac{\sin 5x}{\sin x} = -16\:\frac{19}{400} = -\frac{19}{25}$