Let be a point on the unit circle that corresponds to an angle measured anticlockwise…

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

Problem

Let

P\bigl(-\tfrac{\sqrt 3}{2},\,\tfrac12\bigr)

be a point on the unit circle that corresponds to an angle

\theta

measured anticlockwise from the positive

x

–axis. (i) Find

\sin\theta

\cos\theta

and

\tan\theta

using the coordinates of

P

. (ii) Determine the principal value of

\theta

in degrees as well as in radians for

0\le \theta<2\pi

. (iii) Verify numerically that the point satisfies the identity

\sin^{2}\theta+\cos^{2}\theta=1

. Explain why this identity must hold for every point on the unit circle.