Evaluate the following trigonometric ratios involving a negative or reflex angle.

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

Problem

Evaluate the following trigonometric ratios involving a negative or reflex angle. (i) Express

255^{\circ}

in a form that allows you to use standard exact values. (ii) Find the exact value of

\sin 255^{\circ}

. (iii) Find the exact value of

\cos 255^{\circ}

. (iv) Verify that

\sin 255^{\circ}=-\sin 75^{\circ}

and

\cos 255^{\circ}=-\cos 75^{\circ}

, showing all steps clearly.