A point on the unit circle has ordinate and lies in Quadrant IV

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

A point

Q

on the unit circle has ordinate

y=-\tfrac35

and lies in Quadrant IV. The corresponding angle is

\phi

. (i) Determine the abscissa of

Q

. (ii) Hence find the exact values of

\sin\phi

\cos\phi

and

\tan\phi

. (iii) Without using a calculator, compute

\sin(180^{\circ}-\phi)

\cos(180^{\circ}-\phi)

and

\tan(180^{\circ}-\phi)

. Explain the steps clearly.