QuestionSolve the equation: $\sin^{-1} x = \frac{\pi}{6}$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $\sin^{-1}x = \frac{\pi}{6}$ . We are looking for the exact solution for x

STEP 2

The equation $\sin^{-1}x = \frac{\pi}{6}$ can be interpreted as "x is the sine of $\frac{\pi}{6}$ ".

STEP 3

We can find the value of x by taking the sine of $\frac{\pi}{6}$ .
$x = \sin\left(\frac{\pi}{6}\right)$

STEP 4

The sine of $\frac{\pi}{6}$ is a known value. $x = \sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$ So, the exact solution of the equation is $x = \frac{1}{2}$ .

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