Mathematics

Problem

Let

\theta

be an angle satisfying

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

with

\theta

lying in the second quadrant. Answer the following. a. (i) Find the value of

\cos \theta

. b. (ii) Calculate the value of

2\sin \theta \cos \theta

. c. (iii) Hence determine the exact value of

\sin 2\theta

. Show all steps of your calculation.