Question

Since each inverse trig function can have only one output, we choose the output that falls in a specified interval for each. For each, what interval must the output be in in order for it to be valid?

a. y=sin⁻¹

Answer 1

The output of the inverse sine function, y=sin⁻¹(x), must always fall within the interval [-π/2, π/2] or [-90°, 90°] to satisfy the definition of a function.

Step-by-step explanation:

Intervals for Inverse Trigonometric Functions

The sinusoidal nature of the sine function means it oscillates between -1 and +1. The inverse sine function, represented as y=sin⁻¹(x), must have its output, or angle, fall within a specific range to maintain its function as a true inverse. This allows for each real number in the domain of y=sin⁻¹ to correspond to exactly one angle, satisfying the definition of a function. For y=sin⁻¹, the interval the output must fall in is [-π/2, π/2] or [-90°, 90°] in degrees. This interval encompasses the range where the original sine function is increasing from -1 to +1.