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Draw in graph of y=" cosec"^(-1)("cosec ...

Draw in graph of `y=" cosec"^(-1)("cosec x")`.

Text Solution

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`y = "cosec"^(-1) ("cosec x")`
`rArr" ""cosec "y=" cosec x"`
`rArr" "sin y = sin x`
Hence the graph of `y = "cosec"^(-1)("cosec" x)` is the same as that of `y = sin^(-1)(sin x)`, but excludng points `x=npi, n in Z`, where cosec x is not defined.
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Knowledge Check

  • Range of "cosec"^(-1)x is

    A
    `(-pi/2,pi/2)`
    B
    `[-pi/2,pi/2]`
    C
    `[-pi/2,pi/2]-{0}`
    D
    none of these

  • cosec^(-1)(cos x) is real if

    A
    `xepsilon[-1,1]`
    B
    `xepsilonR`
    C
    `x` is an odd multiple of `(pi)/2`
    D
    `x` is a multiple of `pi`

  • If y="cosec"^(-1) (2x+1),"then "dy/dx=

    A
    ` (2(tan ^(-1) x)^((2)/(3)))/( 3( 1+x^(2)))`
    B
    ` (4(tan ^(-1) x)^((2)/(3)))/( 3( 1+x^(2)))`
    C
    ` (4(tan ^(-1) x)^((4)/(3)))/( 3( 1+x^(2)))`
    D
    ` (4(tan ^(-1) x)^((1)/(3)))/( 3( 1+x^(2)))`

    • Similar Questions

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    Draw the graph of y = " cosec "^(2) x - cot^(2) x. Is f(x) periodic ? If yes, what is its fundamental period ?

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