Home
Class 12
MATHS
Find (dy)/(dx)ifx=a(theta-sintheta) and ...

Find `(dy)/(dx)ifx=a(theta-sintheta) and y=a(1-costheta)dot`

Text Solution

Verified by Experts

`"We have "x=a(theta-sin theta)and y=a (1- cos theta).`
`therefore" "(dx)/("d"theta)=a(1-cos theta) and (dy)/("d"theta)=a sin theta`
`"or "(dy)/(dx)=(dy//"d" theta)/(dx//"d" theta)`
`=(a sin theta)/(a(1-cos theta))`
`=(2sin (theta//2)cos (theta//2))/(2 sin^(2) (theta//2))`
`=cot""(theta)/(2)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Solved Examples|28 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.1|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx) . x= a(theta-sin theta), y= a (1+ cos theta) .

Find (dy)/(dx)," if "x= a(theta+ sin theta), y= a(1- cos theta) .

Find y_2 in each of the following cases: x=a(theta+sintheta) , y=a(1-costheta)

If x=a(theta+sin theta) and y=a(1-costheta) , find (d^2y)/(dx^2)"at"theta=pi/2

If x=a(theta+sin theta) and y=a(1+cos theta) , then find the simplified value of (dy)/(dx) and show that, (dy)/(dx)=-1 , when theta=(pi)/(2) .

Find (dy)/(dx) if x=cos theta - cos 2 theta and" "y = sin theta - sin 2theta

Find (dy)/(dx) if x= 2 cos theta - cos 2theta and y= 2sin theta - sin 2theta.

sintheta - sqrt(3)costheta =1

Find (dy)/(dx), " if "x= a cos theta, y= a sin theta .

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx) . x= a (cos theta+ theta sin theta), y= a (sin theta-theta cos theta) .