Study the signs of trigonometric ratios in different quadrants.

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

Problem

Study the signs of trigonometric ratios in different quadrants. (i) Explain how the

x

and

y

coordinates of a point on the unit circle determine the signs of

\cos \theta

and

\sin \theta

respectively. (ii) Using your explanation in part (i), show that

\tan \theta

is positive in Quadrant III even though both

\sin \theta

and

\cos \theta

are negative there. (iii) Determine the signs (only “+” or “−”) of

\sin(-135^\circ)

\cos(210^\circ)

and

\tan\left(\dfrac{5\pi}{6}\right)

, giving brief reasons for each answer.