alleryStart learning →Solve 2 cos t - 3 = -5 exactly on the interval from 0 to 2 pi.
AIt is t = 0 alone
BIt is t = 2 pi alone
CIt is t = pi alone
DIt is t = pi / 2 alone
Answer & Solution
Correct answer: C. It is t = pi alone
1. Add 3 to both sides to get 2 cos t = -2.
2. Divide by 2 to get cos t = -1.
3. Cosine reaches -1 only at the half turn.
4. On the interval from 0 up to 2 pi that gives the single solution t = pi.
5. The value t = 0 gives cos t = 1, which would make the left side 2 - 3 = -1, not -5.
_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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