A curve is represented parametrically by and

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

A curve is represented parametrically by

x=e^t\cos t

and

y=e^t\sin t

, where

t

is a parameter. Find the relation between

t

and the angle

\alpha

between the tangent to the curve and the

x

-axis. (1)

\frac{\pi}{2}-\alpha

(2)

\frac{\pi}{4}+\alpha

(3)

\alpha-\frac{\pi}{4}

(4)

\frac{\pi}{4}-\alpha