A) \[0\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{2}\]
Correct Answer: D
Solution :
We have,\[x={{e}^{t}}\cos t\]and\[y={{e}^{t}}\sin t\] Therefore, \[\frac{dx}{dt}={{e}^{t}}(\cos t-\sin t)\] and \[\frac{dy}{dt}={{e}^{t}}(\sin t+\cos t)\] \[\therefore \] \[\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{\sin t+\cos t}{\cos t-\sin t}\] \[\Rightarrow \] \[{{\left( \frac{dy}{dx} \right)}_{t=\pi /4}}=\infty =\tan \frac{\pi }{2}\] So, tangent at\[t=\pi /4\]makes with axis of\[x\], the angle is\[\pi /2\].
You need to login to perform this action.
You will be redirected in
3 sec
