Equal Trig Triples

★ 7/10trigonometrySet TheoryTrigonometric IdentitiesCasework

Problem

Suppose

{cos⁡α,cos⁡2α,cos⁡3α}={sin⁡α,sin⁡2α,sin⁡3α}.\{\cos\alpha, \cos 2\alpha, \cos 3\alpha\} = \{\sin\alpha, \sin 2\alpha, \sin 3\alpha\}.

Determine which of the values

α=π8,−3π8,2π3,−π3\alpha = \frac{\pi}{8}, \qquad -\frac{3\pi}{8}, \qquad \frac{2\pi}{3}, \qquad -\frac{\pi}{3}

satisfy this condition, with proof.

Answer

Solution

Difficulty7/10
Topicstrigonometry, Set Theory, Trigonometric Identities, Casework

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