Question

Find the exact value of sin-1(-0.5).

Answer 1

We are asked to evaluate the expression sin-1(-0.5). The answer is an angle with units of degrees or radians. In this case, we use a calculator to evaluate the expression. The answer is -30 degrees or negative pi/6. The angle is valid in the third and fourth quadrants

Answer 2

Answer:   $\dfrac{-\pi}{6}$

Step-by-step explanation:

To find : The exact value of $\sin^{-1}(-0.5)$ .

We know that $\sin^{-1}(\dfrac{1}{2})=\dfrac{\pi}{6}$.

The range of  $\sin^{-1}(x)$ is between $\dfrac{-\pi}{2}\text{ and }\dfrac{\pi}{2}$

Let $t=\sin^{-1}(-0.5)$

$\sin t=-0.5=-\sin(\dfrac{\pi}{6})=\sin(\dfrac{-\pi}{6})\ [\text{Since }}\sin(-x)=-\sin x]$  

$\sin(\dfrac{-\pi}{6})=0.5$

Hence, the principal value of  $\sin^{-1}(-0.5)=\dfrac{-\pi}{6}$