For the equation with

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

For the equation cos⁡2θ=−13\cos 2\theta=-\dfrac13 with 0<θ<2π0<\theta<2\pi, answer the following: (i) Rewrite cos⁡2θ\cos 2\theta entirely in terms of cos⁡θ\cos\theta and form an algebraic equation in cos⁡θ\cos\theta. (ii) Solve the equation obtained in part (i) to find all possible values of cos⁡θ\cos\theta. (iii) Hence determine every value of θ\theta satisfying cos⁡2θ=−13\cos 2\theta=-\dfrac13 in the interval 0<θ<2π0<\theta<2\pi. (iv) For each value of θ\theta found in part (iii), determine the corresponding value of sin⁡θ\sin\theta.

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