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If cos(α) = 1/2, what are the possible values of α in the interval [0, 2π]?

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Question: If cos(α) = 1/2, what are the possible values of α in the interval [0, 2π]?

Options:

  1. π/3, 5π/3
  2. π/4, 3π/4
  3. 0, π
  4. π/6, 11π/6

Correct Answer: π/3, 5π/3

Solution: 

The angles where cos(α) = 1/2 in the interval [0, 2π] are α = π/3 and α = 5π/3.

If cos(α) = 1/2, what are the possible values of α in the interval [0, 2π]?

Practice Questions

Q1
If cos(α) = 1/2, what are the possible values of α in the interval [0, 2π]?
  1. π/3, 5π/3
  2. π/4, 3π/4
  3. 0, π
  4. π/6, 11π/6

Questions & Step-by-Step Solutions

If cos(α) = 1/2, what are the possible values of α in the interval [0, 2π]?
Correct Answer: α = π/3 and α = 5π/3
  • Step 1: Understand that cos(α) = 1/2 means we are looking for angles where the cosine value is 1/2.
  • Step 2: Recall the unit circle and the values of cosine for common angles.
  • Step 3: Identify that cos(π/3) = 1/2. This is one angle we are looking for.
  • Step 4: Remember that cosine is positive in the first and fourth quadrants.
  • Step 5: Find the corresponding angle in the fourth quadrant. This angle is 2π - π/3.
  • Step 6: Calculate 2π - π/3. This gives you 6π/3 - π/3 = 5π/3.
  • Step 7: List the angles found: α = π/3 and α = 5π/3.
  • Trigonometric Functions – Understanding the values of trigonometric functions, specifically the cosine function, and their corresponding angles.
  • Unit Circle – Using the unit circle to determine angles that yield specific cosine values.
  • Periodic Properties – Recognizing the periodic nature of trigonometric functions and identifying all possible angles within a given interval.
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