Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

If $x$ and $y$ are connected parametrically by the equations given in $ x = \sin t, y = \cos 2t $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

$\begin{array}{1 1} -4\cos t \\ -5\sin t \\ 4\sin t \\ -4\sin t \end{array} $

Can you answer this question?

1 Answer

0 votes
  • By chain rule we have $\large\frac{dy}{dx}=\frac{dy}{dt}$$\times\large\frac{dt}{dx}$
Step 1:
Given :
$x=\sin t$
Differentiating with respect to $t$
$\large\frac{dx}{dt}$$=\cos t$
$f'(t)=\cos t$
Step 2:
$y=\cos 2t$
Differentiating with respect to $t$
$\large\frac{dy}{dt}$$=-\sin 2t.2$
$\large\frac{dy}{dt}$$=-2\sin 2t$
$g'(t)=-2\sin 2t$
Step 3:
$\quad\;=-2\sin 2t\times \large\frac{1}{\cos t}$
We know that $\sin 2A=2\sin A\cos A$
Hence $\sin 2t=2\sin t\cos t$
Replacing $\sin 2t$ we get
$\large\frac{dy}{dt}$$=-4\sin t\cos t$
Thus $\large\frac{dy}{dx}=\frac{dy}{dt}$$\times\large\frac{dt}{dx}$
$\qquad\;\;\;\;\;\;=-4\sin t\cos t\times\large\frac{1}{\cos t}$
$\qquad\;\;\;\;\;\;=-4\sin t$
answered May 10, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App