Question

lf the parametric equation of a curve given by $x=e^t\cos t,y=e^t\sin t$, then the tangent to the curve at the point $t=\frac{\pi }{4}$ makes with axis of $x$ the angle.

• A. $0$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is D $\frac{\pi }{2}$

$att=\pi /4$
$y=e^{t}sint$
$\frac{dy}{dl}=e^t(sint+cost)$
$\frac{dx}{dl}=d^t(cost+sint)$
$\frac{dy}{dx}=\frac{sint+cost}{cost-sint}$
$=\alpha$
$\therefore ta{n}^{-1}\left(\infty \right)=\pi /2$