Consider a point on the unit circle

MATHEMATICS · Subjective · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Consider a point

P(\cos \theta,\,\sin \theta)

on the unit circle. (i) Show that a clockwise rotation of

90^{\circ}

carries

P

to a point

R

whose coordinates can be written as

(\sin \theta,\,-\cos \theta)

. (ii) Deduce that the coordinates of the point corresponding to the angle

\theta-\dfrac{\pi}{2}

are

(\sin \theta,\,-\cos \theta)

. (iii) Using part (ii), write the exact coordinates of the point on the unit circle that corresponds to an angle of

300^{\circ}