Give clear reasons for each answer.

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

Problem

Give clear reasons for each answer. (a) Explain why both sin⁡θ\sin\theta and cos⁡θ\cos\theta are positive for every angle θ\theta that lies between 0∘0^\circ and 90∘90^\circ. (b) Using a geometric argument on the unit circle, describe how the numerical value of sin⁡θ\sin\theta changes as θ\theta increases from 0∘0^\circ to 90∘90^\circ. Why does cos⁡θ\cos\theta show the opposite trend over the same interval? (c) Without performing numerical calculations, determine whether tan⁡θ\tan\theta is increasing or decreasing on the interval 0∘<θ<90∘0^\circ<\theta<90^\circ. Justify the answer geometrically.

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