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If x = cos^(-1)(1/2), then what is the value of sin^(-1)(x)?

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Question: If x = cos^(-1)(1/2), then what is the value of sin^(-1)(x)?

Options:

  1. π/3
  2. π/6
  3. π/4
  4. 0

Correct Answer: π/6

Solution: 

Since x = cos^(-1)(1/2) = π/3, then sin^(-1)(1/2) = π/6.

If x = cos^(-1)(1/2), then what is the value of sin^(-1)(x)?

Practice Questions

Q1
If x = cos^(-1)(1/2), then what is the value of sin^(-1)(x)?
  1. π/3
  2. π/6
  3. π/4
  4. 0

Questions & Step-by-Step Solutions

If x = cos^(-1)(1/2), then what is the value of sin^(-1)(x)?
Correct Answer: π/6
  • Step 1: Understand that cos^(-1)(1/2) means we are looking for an angle whose cosine value is 1/2.
  • Step 2: Recall that the angle Ï€/3 (or 60 degrees) has a cosine value of 1/2.
  • Step 3: Therefore, we can say x = Ï€/3.
  • Step 4: Now, we need to find sin^(-1)(x), which means we are looking for an angle whose sine value is x (which is Ï€/3).
  • Step 5: Recall that sin(Ï€/6) = 1/2, so sin^(-1)(1/2) = Ï€/6.
  • Step 6: Therefore, the final answer is sin^(-1)(x) = Ï€/6.
  • Inverse Trigonometric Functions – Understanding the relationship between inverse cosine and inverse sine functions.
  • Angle Values – Knowledge of specific angle values for trigonometric functions, particularly for cos(Ï€/3) and sin(Ï€/6).
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