Mathematics

Problem

Let

\theta

be an angle such that

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

and

\cos \theta=-\dfrac{4}{5}

. Answer the following parts. a. (i) Find

\sin \theta

and justify the sign of the result. b. (ii) Determine

\tan \theta

in simplest form. c. (iii) Using your results, compute

\tan 2\theta

and state clearly whether it is positive or negative.