Question

Find the value of sin -1(-square3/2)

Answer 1

the value of sin⁻¹(-√3/2) is 240 degrees (or 4π/3 radians).

Explanation:

The value of sin⁻¹(-√3/2) can be found using the unit circle or a calculator that has inverse trigonometric functions.

Using the unit circle, we know that sin⁻¹(-√3/2) is the angle θ that has a sine equal to -√3/2.

In the third quadrant of the unit circle, sinθ is negative, so we need to look for an angle in the third quadrant whose sine is -√3/2.

Since sin(60°) = √3/2, we know that sin(240°) = -√3/2. Therefore, sin⁻¹(-√3/2) = 240°.

So, the value of sin⁻¹(-√3/2) is 240 degrees (or 4π/3 radians).