Math  /  Trigonometry

QuestionFind all solutions to each equation in radians. 4+15sec(2θ+2π3)=83+4+3sec(2θ+2π3)4+15 \sec \left(-2 \theta+\frac{2 \pi}{3}\right)=8 \sqrt{3}+4+3 \sec \left(-2 \theta+\frac{2 \pi}{3}\right) A) {3π+6πn,π4πn}\left\{3 \pi+6 \pi n, \frac{\pi}{4}-\pi n\right\} B) {7π12πn,π4πn}\left\{-\frac{7 \pi}{12}-\pi n, \frac{\pi}{4}-\pi n\right\} C) {3π+6πn}\{3 \pi+6 \pi n\} D) {7π12πn,3π+6πn}\left\{-\frac{7 \pi}{12}-\pi n, 3 \pi+6 \pi n\right\}

Studdy Solution
Our solutions are θ=π4πn\theta = \frac{\pi}{4} - \pi n and θ=7π12πn\theta = -\frac{7\pi}{12} - \pi n, which matches option B!

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