If x=10(t- ),y=12(1- ), find dy dx . - Vidyadip

Question

If $\text{x}=10(\text{t}-\sin\text{t}),\text{y}=12(1-\cos\text{t}),$ find $\frac{\text{dy}}{\text{dx}}.$

✓

Answer

Here, $\text{x}=10(\text{t}-\sin\text{t}),\text{y}=12(1-\cos\text{t})$
$\Rightarrow\frac{\text{dx}}{\text{dt}}=10(1-\cos\text{t})\ ...(\text{i})$
$\Rightarrow\frac{\text{dx}}{\text{dt}}=12(\sin\text{t})\ ...(\text{ii})$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\frac{\text{dy}}{\text{dt}}}{\frac{\text{dx}}{\text{dt}}}=\frac{12(\sin\text{t})}{10(1-\cos\text{t})}$ From equation (i) and (ii)
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{12\sin\frac{\text{t}}{2}\cdot\cos\frac{\text{t}}{2}}{10\sin^2\frac{\text{t}}{2}}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{6}{5}\cot\frac{\text{t}}{2}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Two cards are drawn simultaneosly from a well shuffled deck of 52 cards. Find the probability distribution of the number of the successes, when getting a spade is considered a success.

If $\text{y}=\text{x}\sin(\text{a}+\text{y}),$ prove that $\frac{\text{dx}}{\text{dx}}=\frac{\sin^2(\text{a}+\text{y})}{\sin(\text{a}+\text{y})-\text{y}\cos(\text{a}+\text{y})}$

$\int\frac{\text{x}}{\sqrt{\text{x}+\text{a}}-\sqrt{\text{x}+\text{b}}}\text{dx}$

If AD is the median of $\triangle\text{ABC},$ using vectors, prove that $\text{AB}^2+\text{AC}^2=2\big(\text{AD}^2+\text{CD}^2\big).$

Maximise Z = 3x + 5y
such that $\text{x}+3\text{y}\geq3,\ \text{x}+\text{y}\geq2,\ \text{x},\ \text{y}\geq0.$

Verify Rolle's theorem for the following function on the indicated intervals

$\text{f}(\text{x})=\cos2\Big(\text{x}-\frac{\pi}{4}\Big)\text{ on }\Big[0,\frac{\pi}{2}\Big]$

Find the equation of the curve which passes through the point $(1, \frac{\pi}{4})$ and tangent at any point 0f which makes an angle $\tan^{-1}\Big(\frac{\text{y}}{\text{x}}-\cos^{2}\frac{\text{y}}{\text{x}}\Big)$ with x-axis.

In the following, find the value of the constant k so that the given function is continuous at the indicated point:
$\text{f(x)}=\begin{cases}\frac{\text{x}^2+\text{x}^2-16\text{x}+20}{(\text{x}-2)^2},&\text{ x}\neq2\\\text{k},&\text{x}=2\end{cases}$

Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\sin\text{x}|\sin\text{x}|\text{dx}$

If $\text{A}=\begin{bmatrix}3&-5\\-4&2\end{bmatrix},$ find A² - 5A - 14.