Answer the following questions about the behaviour of trigonometric ratios at (or…

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

Problem

Answer the following questions about the behaviour of trigonometric ratios at

90^{\circ}

(or

\tfrac{\pi}{2}

radians). (i) State the definitions of

\tan x

and

\sec x

in terms of

\sin x

and

\cos x

. (ii) Using these definitions, explain clearly why

\tan 90^{\circ}

and

\sec 90^{\circ}

are undefined, even though

\sin 90^{\circ}

and

\cos 90^{\circ}

are perfectly well defined. (iii) Describe, with reasons, what happens to the numerical value and sign of

\tan x

x

approaches

90^{\circ}

from the left and from the right. Your answer should refer to the signs of

\sin x

and

\cos x

in the appropriate quadrants.