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Evaluate sin^(-1)(sin(π/4)).

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Question: Evaluate 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

Evaluate sin^(-1)(sin(π/4)).

Practice Questions

Q1
Evaluate sin^(-1)(sin(π/4)).
  1. π/4
  2. 3π/4
  3. π/2
  4. 0

Questions & Step-by-Step Solutions

Evaluate sin^(-1)(sin(π/4)).
  • Step 1: Understand what sin(π/4) means. The sine of π/4 (or 45 degrees) is √2/2.
  • Step 2: Now we need to find sin^(-1)(√2/2). This means we are looking for the angle whose sine is √2/2.
  • Step 3: The angle that has a sine of √2/2 is π/4 (or 45 degrees).
  • Step 4: Therefore, sin^(-1)(sin(π/4)) = sin^(-1)(√2/2) = π/4.
  • Inverse Trigonometric Functions – Understanding how the inverse sine function (sin^(-1)) operates within its principal range.
  • Principal Value – Recognizing that the output of sin^(-1)(x) is restricted to the range [-π/2, π/2].
  • Trigonometric Identities – Applying the identity that relates sine and its inverse.
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