The range of sin^(-1)(x) is:

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Question: The range of sin^(-1)(x) is:

Options:

Correct Answer: [-π/2, π/2]

Solution:

The range of sin^(-1)(x) is [-π/2, π/2].

The range of sin^(-1)(x) is:

The range of sin^(-1)(x) is:

Step 1: Understand what sin^(-1)(x) means. It is the inverse sine function, also known as arcsin(x).
Step 2: Know that the sine function (sin) takes an angle and gives a value between -1 and 1.
Step 3: The inverse sine function (sin^(-1)(x)) takes a value between -1 and 1 and gives back an angle.
Step 4: The angles returned by sin^(-1)(x) are limited to a specific range to ensure that each value corresponds to only one angle.
Step 5: The range of angles for sin^(-1)(x) is from -π/2 to π/2 (in radians).
Step 6: Therefore, the range of sin^(-1)(x) is written as [-π/2, π/2].

Inverse Trigonometric Functions – Understanding the properties and ranges of inverse trigonometric functions, specifically the arcsine function.
Range of Functions – Identifying the output values (range) of a function based on its definition and domain.