Let be an acute angle for which

MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Let

\theta

be an acute angle for which

\tan\theta = \dfrac{p}{q}

, where

p

and

q

are positive real numbers. (i) Express

\sin\theta

and

\cos\theta

separately in terms of

p

and

q

only. (ii) Using the expressions from part (i), verify that

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

. (iii) If

p = 7

and

q = 24

, compute the numerical values of

\sin\theta

and

\cos\theta

, and check that they satisfy the equation obtained in part (ii).