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The value of sin^(-1)(√3/2) is:

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Question: The value of sin^(-1)(√3/2) is:

Options:

  1. π/3
  2. π/6
  3. π/4
  4. π/2

Correct Answer: π/3

Solution: 

sin^(-1)(√3/2) corresponds to the angle whose sine is √3/2, which is π/3.

The value of sin^(-1)(√3/2) is:

Practice Questions

Q1
The value of sin^(-1)(√3/2) is:
  1. π/3
  2. π/6
  3. π/4
  4. π/2

Questions & Step-by-Step Solutions

The value of sin^(-1)(√3/2) is:
  • Step 1: Understand that sin^(-1)(x) means 'the angle whose sine is x'.
  • Step 2: Identify the value we have, which is √3/2.
  • Step 3: Recall the common angles and their sine values. The sine of π/3 (or 60 degrees) is √3/2.
  • Step 4: Conclude that sin^(-1)(√3/2) is the angle π/3.
  • Inverse Trigonometric Functions – Understanding how to find angles corresponding to specific sine values using the arcsine function.
  • Special Angles – Knowledge of common angles and their sine values, particularly π/3 and its sine value of √3/2.
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