AP EAMCET · Maths · Application of Derivatives
If \(\theta\) is the angle made by the normal drawn to the curve \(\mathrm{x}=\mathrm{e}^{\mathrm{t}} \cos \mathrm{t}, \mathrm{y}=\mathrm{e}^{\mathrm{t}} \sin \mathrm{t}\) at the point \((1,0)\), with the \(\mathrm{X}\)-axis, then \(\theta=\)
- A \(\pi / 2\)
- B \(\pi / 4\)
- C \(3 \pi / 2\)
- D \(3 \pi / 4\)
Answer & Solution
Correct Answer
(D) \(3 \pi / 4\)
Step-by-step Solution
Detailed explanation
\(\because x=e^t \cos t, \mathrm{y}=e^t \sin t\) \(\frac{d x}{d t}=e^t(\cos t-\sin t)\) and \(\frac{d y}{d t}=e^t(\sin t+\cos t)\) Now, \(\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{e^t(\sin t+\cos t)}{e^t(\cos t-\sin t)}\)…
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