Find the value of sin^(-1)(sin(π/4)).

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Question: Find the value of sin^(-1)(sin(π/4)).

Options:

Correct Answer: π/4

Solution:

Since sin(π/4) = 1/√2, sin^(-1)(1/√2) = π/4.

Find the value of sin^(-1)(sin(π/4)).

Find the value of sin^(-1)(sin(π/4)).

Step 1: Understand that sin^(-1) is the inverse function of sin. It gives us the angle whose sine is a given value.
Step 2: Calculate sin(π/4). We know that π/4 radians is equal to 45 degrees.
Step 3: Find the sine of 45 degrees (or π/4 radians). The value is 1/√2.
Step 4: Now we need to find sin^(-1)(1/√2). This means we are looking for the angle whose sine is 1/√2.
Step 5: The angle that has a sine of 1/√2 is π/4 (or 45 degrees).
Step 6: Therefore, sin^(-1)(sin(π/4)) = sin^(-1)(1/√2) = π/4.

Inverse Trigonometric Functions – Understanding how the inverse sine function (sin^(-1)) operates within its principal range.
Trigonometric Values – Knowledge of the sine values for common angles, particularly π/4.