Question

if x= cos theta and y= sin theta then find dy/dx​

Answer 1

Step-by-step explanation:

dy/dx=dy/dtheta/(dx/dtheta)=cos(th)/(-sin(th))=-cot(th) which is also -x/y, since x^2+y^2=cos^2+sin^2=1 and differentiation gives 2*x*dx+2*y*dy=0 so dy/dx=-x/y.

Answer 2

The value of $\frac{dy}{dy} \ is \ \frac{x}{(-y)}$ .

Step-by-step explanation:

Given:

$x=cos\theta$

$y= sin\theta$

To Find:

The value of $\frac{dy}{dx}$.

Formula Use:

$\frac{dy}{dx}$ denotes the differentiation of y with respect to the variable x.

$x=cos\theta$

then $\frac{dx}{d\theta} = -sin\theta$     --------------------------------------- formula no .01

$y= sin\theta$

then $\frac{dy}{d\theta} = cos \theta$   -----------------------------------------  formula no.02

$\frac{dy}{dx} =\frac{(\frac{dy}{d\theta}) }{(\frac{dx}{d\theta}) }$       ------------------------------------------------ formula no.03

Solution:

As given -    $x=cos\theta$

Applying formula no.01

   $\frac{dx}{d\theta} = -sin\theta$    ---------    equation no.01

As given-    $y= sin\theta$

$\frac{dy}{d\theta} = cos \theta$           ------------ equation no.02

To find  - the value of $\frac{dy}{dx}$.

Applying formula no.03. and putting the value of $\frac{dy}{d\theta}$   and $\frac{dx}{d\theta}$.

$\frac{dy}{dx} =\frac{(\frac{dy}{d\theta}) }{(\frac{dx}{d\theta}) }$

    $= \frac{cos\theta}{(-sin\theta)}$

$\frac{dy}{dy} = \frac{cos\theta}{(-sin\theta)}$

Putting the value of $y= sin\theta$ and $x=cos\theta$ , we get.

$\frac{dy}{dy} = \frac{x}{(-y)}$

Thus, The value of   $\frac{dy}{dy} \ is \ \frac{x}{(-y)}$ .