Question

The inverse sine, inverse cosine, and inverse tangent functions have the following domains and ranges. (Enter your answers in interval notation.)

The function sin−1 has domain _______ and range __________

Answer 1

The function sin⁻¹ has a domain of [-1, 1] and a range of [-π/2, π/2].

Step-by-step explanation:

Domain of sin⁻¹(x): The domain of sin⁻¹(x) is [-1, 1] because the sine function is defined for values between -1 and 1.

Range of sin⁻¹(x): The range of sin⁻¹(x) is [-π/2, π/2] since the inverse sine function returns values in the interval [-π/2, π/2], representing angles between -90 and 90 degrees.

Interval Notation: Express the domain and range in interval notation: Domain = [-1, 1], Range = [-π/2, π/2].