In a right–angled triangle

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

Problem

In a right–angled triangle, one of the acute angles is denoted by

\theta

and it is given that

\cos\theta = \dfrac{3}{5}

. Answer the following questions in the order given. (i) State the fundamental trigonometric identity that relates

\sin\theta

and

\cos\theta

. (ii) Using the identity, calculate the value of

\sin\theta

. (iii) Explain why the value of

\sin\theta

obtained in part (ii) must be positive for the given situation. (iv) Verify numerically that

\sin^{2}\theta + \cos^{2}\theta = 1

for the pair of ratios found.