Answer the following questions concerning the trigonometric equation

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Answer the following questions concerning the trigonometric equation tan⁡θ=tan⁡α\tan\theta = \tan\alpha, where α\alpha is a fixed angle. (i) Explain why the function tan⁡θ\tan\theta repeats its values after an increase of π\pi radians, whereas sin⁡θ\sin\theta and cos⁡θ\cos\theta repeat after 2π2\pi radians. (ii) Using the property stated in part (i), obtain the general solution of the equation tan⁡θ=tan⁡α\tan\theta = \tan\alpha. (iii) How many distinct solutions does the equation tan⁡θ=tan⁡60∘\tan\theta = \tan 60^{\circ} have in any interval of length π\pi? Justify your answer.

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