Question:
Find $\frac{\mathrm{dy}}{\mathrm{dx}}$, when
If $x=10(t-\sin t), y=12(1-\cos t)$, find $\frac{d y}{d x}$
Solution:
Here, $x=10(t-\sin t) y=12(1-\cos t)$
$\frac{\mathrm{dx}}{\mathrm{dt}}=10(1-\cos \mathrm{t})$ (1)
$\frac{d y}{d t}=12(\sin t) \ldots \ldots(2)$
$\frac{d y}{d x}=\frac{\frac{d y}{d x}}{\frac{d x}{d t}}=\frac{12(\sin t)}{10(1-c o s t)} \mid$ from equation 1 and 2
$\frac{d y}{d x}=\frac{12 \sin \frac{t}{2} \cdot \cos t / 2}{10 \sin ^{2} t / 2}$
$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{6}{5} \cot \frac{\mathrm{t}}{2}$
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