Triangle explanation based on complementary angles In right–angled triangle

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

Problem

Triangle explanation based on complementary angles In right–angled triangle PQRPQR, ∠Q=90∘\angle Q = 90^{\circ} and ∠P=θ\angle P = \theta. The side opposite ∠P\angle P is QRQR, the side adjacent to ∠P\angle P is PQPQ and the hypotenuse is PRPR. (i) Write sin⁡(90∘−θ)\sin(90^{\circ}-\theta) in terms of the sides of the triangle. (ii) Write cos⁡θ\cos \theta in terms of the same sides. (iii) Explain, using the results of parts (i) and (ii), why sin⁡(90∘−θ)=cos⁡θ\sin(90^{\circ}-\theta)=\cos\theta for every acute angle θ\theta.

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