Answer the following questions related to angles on the unit circle.

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

Problem

Answer the following questions related to angles on the unit circle. (i) Define the reference angle of any real‐valued angle

\theta

. (ii) Without using a calculator, determine the reference angle of

235^{\circ}

. State clearly the quadrant in which the terminal side of

235^{\circ}

lies. (iii) Using the quadrant identified in part (ii), explain whether

\sin 235^{\circ}

and

\cos 235^{\circ}

are positive or negative. Give reasons for each sign.