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

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

Options:

  1. √3/2
  2. 1/2
  3. 0
  4. 1

Correct Answer: √3/2

Solution: 

Let θ = cos^(-1)(1/2). Then cos(θ) = 1/2, which corresponds to θ = π/3. Therefore, sin(θ) = sin(π/3) = √3/2.

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

Practice Questions

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

Questions & Step-by-Step Solutions

Find the value of sin(cos^(-1)(1/2)).
Correct Answer: √3/2
  • Step 1: Understand that cos^(-1)(1/2) means we are looking for an angle θ such that the cosine of θ equals 1/2.
  • Step 2: Recall that cos(π/3) = 1/2. Therefore, we can say θ = π/3.
  • Step 3: Now, we need to find sin(θ). Since we found θ = π/3, we will calculate sin(π/3).
  • Step 4: Recall the value of sin(π/3). It is known that sin(π/3) = √3/2.
  • Step 5: Therefore, the value of sin(cos^(-1)(1/2)) is √3/2.
  • Inverse Trigonometric Functions – Understanding how to interpret and evaluate inverse trigonometric functions, specifically cos^(-1) in this case.
  • Trigonometric Identities – Applying the relationship between sine and cosine, particularly using the identity sin(θ) = √(1 - cos²(θ)).
  • Unit Circle – Knowledge of the unit circle and the corresponding angles and their sine and cosine values.
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