Let be a fixed real number

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Let α\alpha be a fixed real number. Answer the following questions related to the trigonometric equation sin⁡θ=sin⁡α\sin\theta = \sin\alpha. (i) State the complete set of real solutions of the equation sin⁡θ=sin⁡α\sin\theta = \sin\alpha in terms of α\alpha and an integer parameter nn. (ii) Prove that the expression obtained in part (i) includes every possible solution and that no other solutions exist. (iii) Using the result of part (i), write all values of θ\theta in the interval 0≤θ<2π0 \le \theta < 2\pi that satisfy sin⁡θ=sin⁡30∘\sin\theta = \sin 30^{\circ}.

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