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

Practice Questions

Q1
If x = cos^(-1)(1/2), what is sin(x)?
  1. √3/2
  2. 1/2
  3. 0
  4. 1

Questions & Step-by-Step Solutions

If x = cos^(-1)(1/2), what is sin(x)?
  • Step 1: Understand that cos^(-1)(1/2) means we are looking for an angle x whose cosine is 1/2.
  • Step 2: Recall the unit circle or the special angles in trigonometry. The angle x that has a cosine of 1/2 is π/3 (or 60 degrees).
  • Step 3: Now that we have x = π/3, we need to find sin(x).
  • Step 4: Use the known value of sin(π/3). From trigonometric values, sin(π/3) = √3/2.
  • Step 5: Therefore, sin(x) = sin(π/3) = √3/2.
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