Answer the following questions about special acute angles.

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Answer the following questions about special acute angles. (i) Write the exact values of

\sin30^{\circ}

and

\cos30^{\circ}

. (ii) If

\sin\theta=\dfrac{1}{2}

where

0^{\circ}<\theta<90^{\circ}

, determine the value of

\theta

and give a short reason for your choice. (iii) Using the value of

\theta

obtained in part (ii), verify that

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