Question

Solve the equation: |3 sin 3/2 x| = 1 + 6x/5π

Answer 1

Solve the equation: $|3\sin 3 / 2x| = 1 + 6x / 5\pi$

Sketching on the same diagram the graphs of $y = \left|3\sin \frac{3x}{2}\right|$ and $y = 1 + \frac{6x}{\pi}$

$\left|\sin \frac{3x}{2}\right| = 1 + \frac{6x}{\pi}$

The graph of the function $y = \sin x$

The amplitude $y = 3\sin \frac{3x}{2}$ is 3

The period $y = 3\sin \frac{3x}{2}$ is

$\frac{2\pi}{\frac{3}{2}} = \frac{4\pi}{3}$

The graph of the function $y = 3\sin \frac{3x}{2}$

The graphs of the functions $y = \left|3\sin \frac{3x}{2}\right|$ and $y = 1 + \frac{6x}{\pi}$

So for $0 < x < 2$ there are 2 solutions