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Find the value of sin^(-1)(sin(π/3)).

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Question: Find the value of sin^(-1)(sin(π/3)).

Options:

  1. π/3
  2. 2π/3
  3. π/6
  4. 0

Correct Answer: π/3

Solution: 

Since π/3 is in the range of sin^(-1), sin^(-1)(sin(π/3)) = π/3.

Find the value of sin^(-1)(sin(π/3)).

Practice Questions

Q1
Find the value of sin^(-1)(sin(π/3)).
  1. π/3
  2. 2π/3
  3. π/6
  4. 0

Questions & Step-by-Step Solutions

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