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If x=a(theta+sintheta) and y=a(1-costhet...

If `x=a(theta+sintheta)` and `y=a(1-costheta)`, find `dy//dx`.

A

`(sintheta)/(1+costheta)`

B

`(costheta)/(1+sintheta)`

C

`(1+costheta)/(sintheta)`

D

`(sintheta)/(1-costheta)`

Text Solution

Verified by Experts

The correct Answer is:
1
`(dx)/(d theta)=a(1+costheta),(dy)/(d theta)=a(0+sintheta)`
`(dy)/(dx)=(dy)/(d theta)//(d theta)/(dx)=(asintheta)/(a(1+costheta))`
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Find dy/dx if x=a(theta+sintheta), y=a(1-costheta)

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Knowledge Check

  • If x=a(theta+sintheta) and y=a(1-costheta) , then (dy)/(dx) is equal to

    A
    `tan""(theta)/(2)`
    B
    `cot""(theta)/(2)`
    C
    `tantheta`
    D
    `cottheta`

  • If y=a(theta+sintheta),x=a(1-costheta)," then "(dy)/(dx)=

    A
    `cot((theta)/(2))`
    B
    `-cot((theta)/(2))`
    C
    `-tan((theta)/(2))`
    D
    `tan((theta)/(2))`

  • If x=theta-sintheta" and "y=1-costheta," then "(d^(2)y)/(dx^(2))=

    A
    `(-1)/(4sin^(4)(theta/(2)))`
    B
    `(-1)/(2sin^(2)(theta/(2)))`
    C
    `tantheta`
    D
    `cottheta`

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    If x=k(theta+sintheta) and y=k(1+costheta) . then what is the derivative of y with respect to x at theta=pi//2 ?

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