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The value of sin^(-1)(sin(π/4)) is:

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Question: The value of sin^(-1)(sin(π/4)) is:

Options:

  1. π/4
  2. 3π/4
  3. 0
  4. π/2

Correct Answer: π/4

Solution: 

Since π/4 is in the range of sin^(-1), sin^(-1)(sin(π/4)) = π/4.

The value of sin^(-1)(sin(π/4)) is:

Practice Questions

Q1
The value of sin^(-1)(sin(π/4)) is:
  1. π/4
  2. 3π/4
  3. 0
  4. π/2

Questions & Step-by-Step Solutions

The value of sin^(-1)(sin(π/4)) is:
  • Step 1: Understand what sin(π/4) means. π/4 is an angle in radians, which is equal to 45 degrees.
  • Step 2: Calculate sin(π/4). The sine of 45 degrees (or π/4 radians) is √2/2.
  • Step 3: Now, we need to find sin^(-1)(√2/2). This means we are looking for the angle whose sine is √2/2.
  • Step 4: The angle that has a sine of √2/2 and is within the range of sin^(-1) (which is from -π/2 to π/2) is π/4.
  • Step 5: Therefore, sin^(-1)(sin(π/4)) = π/4.
  • Inverse Trigonometric Functions – Understanding how inverse functions work, particularly the range and domain of sin^(-1) and sin.
  • Principal Values – Recognizing that the inverse sine function returns values within a specific range, typically [-π/2, π/2].
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