Mathematics

Problem

Let

\theta

be an angle such that

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

and

\theta

lies in the second quadrant. Answer the following: a. (i) Find

\cos\theta

and

\tan\theta

. b. (ii) Determine the exact values of

\csc\theta,\;\sec\theta

and

\cot\theta

. c. (iii) Verify that

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

for the values obtained.