Mathematics

Problem

For an angle

\theta

it is given that

\tan \theta = \dfrac{3}{4}

and that

\theta

lies in the third quadrant. a. (i) Determine the exact values of

\sin \theta

and

\cos \theta

. b. (ii) Hence find

\csc \theta,\; \sec \theta

and

\cot \theta

. c. (iii) Using the results obtained, verify numerically that

\sin ^2\!\theta + \cos ^2\!\theta = 1