## The domain of sin−1(x) is__________and the range is__________

### [−1,1]; [−π/2,π/2]

The domain of sin⁻¹(x) is [-1, 1].

This is because sin⁻¹(x) is the inverse function of sine, which has a range of [-1, 1]. Therefore, when we take the inverse function of sin, we need to restrict the domain to [-1, 1] so that every value of x in the domain will have a corresponding value in the range.

The range of sin⁻¹(x) is [-π/2, π/2].

This is because sin⁻¹(x) gives the angle (in radians) whose sine is x. The sine function has a range of [-1, 1], and the angle whose sine is 1 is π/2 (or 90 degrees), while the angle whose sine is -1 is -π/2 (or -90 degrees). Therefore, the range of sin⁻¹(x) is [-π/2, π/2].

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