Question

Q16 The tangent to the curve given by x = e' cost, y = e' sint at t = pie/4, makes with
x-axis an angle of
(a) o
(b) pi/4
(c) pi/3
(d) pi/2
Оа
Od

Answer 1

Given :  Tangent to the curve x = e' cost, y = e' sint at t = pie/4,

To find : x-axis of an angle of the tangent

Solution :

at t = $\frac{\pi }{4}$

y = e'sin t

dy/dl =$e^{t}$(sin t + cos t) ---->(1)

x = e' cos t

dx/dl = e t ( cos t - sin t) ---->(2)

dividing by (1) by (2)

dy/dx = (sin t + cos t) / (cos t - sin t) = ∝

$tan^{-1}$ (∝) = $\frac{\pi }{2}$

Therefore,the answer is option(d) $\frac{\pi }{2}$