Question

The equation of the curve is given by $x=e^t\sin t$, $y=e^t\cos t$. The inclination of the tangent to the curve at the point $t=\frac{\pi }{4}$ is

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

Answer 1

The correct option is D $0$

$dx=e^t(\cos t+\sin t).dt$
$dy=e^t[\cos t-\sin t).dt$
Hence
${\frac{dy}{dx}}_{t=\frac{\pi }{4}}$

$={\frac{\cos t-\sin t}{\cos t+\sin t}}_{t=\frac{\pi }{4}}$

$=0$