Mathematics

Problem

Given that

\cos\theta=-\dfrac{2}{5}

and

\dfrac{\pi}{2}<\theta<\pi

, answer the following. a. (i) Determine

\sin\theta

. b. (ii) Hence find

\tan\theta

\sec\theta

\csc\theta

and

\cot\theta

. c. (iii) Verify that

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

for this value of

\theta