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.
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