If the parametric equation of a curve given by $x = {e^t}\;{\rm{cost}},\;y = {e^t}\sin t$ then the tangent to the curve at the point $t = \pi /4$ makes with axis of $x$ the angle

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

If the parametric equation of a curve given by

x = {e^t}\;\mathrm{cost},\;y = {e^t}\sin t

then the tangent to the curve at the point

t = \pi /4

makes with axis of

x

the angle

View answer and explanation

Correct option: D

\frac{\pi }{2}

Option D (

\frac{\pi}{2}

) is correct because the tangent at t =

\frac{\pi}{4}

has an infinite slope, indicating a vertical line.

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