Mathematics

Problem

Let

\theta

be an angle such that

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

and

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

. a. (i) Find

\cos \theta

. b. (ii) Determine

\tan \theta

. c. (iii) Evaluate

\sin^{2}\!\theta + \cos^{2}\!\theta

. d. (iv) Hence compute

1 - 2\sin^{2}\!\theta