alleryStart learning →On the interval from 0 to 2 pi, which angles satisfy cos t = 1/2?
Api/3 and 5 pi/3
Bpi/6 and 5 pi/6
Cpi/3 and 2 pi/3
Dpi/6 and 11 pi/6
Answer & Solution
Correct answer: A. pi/3 and 5 pi/3
1. Cosine equals 1/2 at the reference angle pi/3.
2. Cosine is positive in quadrants I and IV, so both solutions sit there.
3. The quadrant I angle is pi/3 and the quadrant IV angle is 2 pi - pi/3 = 5 pi/3.
4. The pair pi/3 and 2 pi/3 places one solution in quadrant II, where cosine is negative, so it cannot be right.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.5 Solving Trigonometric Equations_
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