Mathematics

Problem

An angle

\theta

satisfies

\sin \theta = -\dfrac{\sqrt{3}}{2}

with

0^{\circ} < \theta \le 1080^{\circ}

. Answer the following without using a calculator. a. (i) List all values of

\theta

(in degrees) that satisfy the given condition within the stated interval. b. (ii) For each value of

\theta

obtained in part (i), write the corresponding exact values of

\cos \theta

and

\tan \theta

. Simplify your answers. c. (iii) Taking the smallest positive value of

\theta

from part (i), verify that

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

by direct substitution of the exact values found.