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

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

Options:

  1. √3/2
  2. 1/2
  3. 0
  4. 1

Correct Answer: √3/2

Solution: 

If x = cos^(-1)(1/2), then x = Ο€/3, thus sin(x) = sin(Ο€/3) = √3/2.

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 Ο€/3 (or 60 degrees).
  • Step 3: Now that we have x = Ο€/3, we need to find sin(x).
  • Step 4: Use the known value of sin(Ο€/3). From trigonometric values, sin(Ο€/3) = √3/2.
  • Step 5: Therefore, sin(x) = sin(Ο€/3) = √3/2.
  • Inverse Trigonometric Functions – Understanding how to use inverse cosine to find angles and their corresponding sine values.
  • Trigonometric Values – Knowledge of standard angles and their sine and cosine values.
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