Mathematics

Problem

For an acute angle

\theta

, the value of

\sin\theta

is given. Answer the following questions. a. (i) State the fundamental trigonometric identity that relates

\sin\theta

and

\cos\theta

. b. (ii) If

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

, find

\cos\theta

. c. (iii) Explain why the value of

\cos\theta

obtained in (ii) is positive. d. (iv) Using the values of

\sin\theta

and

\cos\theta

, verify numerically that

1 + \tan^{2}\theta = \sec^{2}\theta

for this angle.