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

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

Options:

  1. π/3
  2. 2Ï€/3
  3. π/4
  4. π/6

Correct Answer: 2Ï€/3

Solution: 

x = cos^(-1)(-1/2) = 2Ï€/3

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

Practice Questions

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

Questions & Step-by-Step Solutions

If x = cos^(-1)(-1/2), what is the value of x?
  • Step 1: Understand that cos^(-1)(-1/2) means we are looking for an angle x whose cosine value is -1/2.
  • Step 2: Recall the unit circle and the values of cosine for common angles. The cosine of 120 degrees (or 2Ï€/3 radians) is -1/2.
  • Step 3: Therefore, we can conclude that x = 2Ï€/3 is the angle we are looking for.
  • Inverse Trigonometric Functions – Understanding how to evaluate the inverse cosine function and its range.
  • Unit Circle – Knowledge of the unit circle and the angles corresponding to specific cosine values.
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