Consider the angle in standard position.

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

Problem

Consider the angle

\alpha=\dfrac{5\pi}{3}\text{ rad}

in standard position. (i) Convert

\alpha

to degrees and identify the quadrant in which its terminal side lies. (ii) Explain, with reference to the unit circle, why

\sin\alpha

and

\cos\alpha

have the signs obtained in part (i). (iii) For any angle

\beta

whose terminal side lies in the same quadrant as

\alpha

, state the possible signs of

\tan\beta

and

\sec\beta

, giving reasons based on coordinate signs.