Consider an acute angle (that is, ).

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Consider an acute angle θ\theta (that is, 0∘<θ<90∘0^\circ<\theta<90^\circ). (i) State the relationship between sin⁡θ\sin\theta and cos⁡θ\cos\theta that is obtained from the Pythagorean theorem. (ii) Using the relationship stated in part (i), explain why the numerical value of sin⁡θ\sin\theta can never be greater than 11 for an acute angle. (iii) As the value of sin⁡θ\sin\theta increases in the interval 0∘<θ<90∘0^\circ<\theta<90^\circ, explain how cos⁡θ\cos\theta changes. Support your answer with reference to the relationship stated in part (i).

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