Solve for t x=sin(3t)

$x = \sin (3 t)$

Rewrite the equation as $\sin (3 t) = x$ .

$\sin (3 t) = x$

Take the inverse sine of both sides of the equation to extract $t$ from inside the sine.

$3 t = \arcsin (x)$

Divide each term in $3 t = \arcsin (x)$ by $3$ and simplify.

Divide each term in $3 t = \arcsin (x)$ by $3$ .

$\frac{3 t}{3} = \frac{\arcsin (x)}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 t}{3} = \frac{\arcsin (x)}{3}$

Divide $t$ by $1$ .

$t = \frac{\arcsin (x)}{3}$