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What is the value of sin^(-1)(sin(π/4))?

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Question: What is the value of sin^(-1)(sin(π/4))?

Options:

  1. π/4
  2. 3π/4
  3. π/2
  4. 0

Correct Answer: π/4

Solution: 

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

What is the value of sin^(-1)(sin(π/4))?

Practice Questions

Q1
What is the value of sin^(-1)(sin(π/4))?
  1. π/4
  2. 3π/4
  3. π/2
  4. 0

Questions & Step-by-Step Solutions

What is the value of sin^(-1)(sin(π/4))?
Correct Answer: π/4
  • 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 is π/4 (or 45 degrees).
  • Step 5: Check if π/4 is within the range of the sin^(-1) function. The range of sin^(-1) is from -π/2 to π/2, and π/4 is within this range.
  • Step 6: Since π/4 is in the range, we can conclude that sin^(-1)(sin(π/4)) = π/4.
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