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Find the value of sin^(-1)(√3/2) + cos^(-1)(1/2).

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Question: Find the value of sin^(-1)(√3/2) + cos^(-1)(1/2).

Options:

  1. π/3
  2. π/2
  3. π/4
  4. π/6

Correct Answer: π/3

Solution: 

sin^(-1)(√3/2) = π/3 and cos^(-1)(1/2) = π/3. Therefore, the sum is π/3 + π/3 = 2π/3.

Find the value of sin^(-1)(√3/2) + cos^(-1)(1/2).

Practice Questions

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

Questions & Step-by-Step Solutions

Find the value of sin^(-1)(√3/2) + cos^(-1)(1/2).
  • Step 1: Understand the notation sin^(-1)(x) and cos^(-1)(x). These represent the inverse sine and inverse cosine functions, respectively.
  • Step 2: Find the angle whose sine is √3/2. This is sin^(-1)(√3/2). The angle is π/3 (or 60 degrees).
  • Step 3: Find the angle whose cosine is 1/2. This is cos^(-1)(1/2). The angle is also π/3 (or 60 degrees).
  • Step 4: Add the two angles together: π/3 + π/3.
  • Step 5: Simplify the sum: π/3 + π/3 = 2π/3.
  • Inverse Trigonometric Functions – Understanding the values of sin^(-1) and cos^(-1) for specific angles.
  • Angle Addition – Adding angles derived from inverse trigonometric functions.
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