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If alpha = 3 sin^(-1) ((6)/(11) and beta...

If `alpha = 3 sin^(-1) ((6)/(11) and beta = 3 cos^(-1) ((4)/(9))`, where the inverse trigonometric functions take only the principal values, then the correct options (s) is (are)

A

`cos beta gt 0`

B

`sin beta lt 0`

C

`cos ( alpha + beta) gt0`

D

`cos alpha lt 0`

Text Solution

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The correct Answer is:
B, C, D
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Knowledge Check

  • Principal value of sin^(-1) (-(1)/(2)) + cos^(-1) (-(1)/(2)) is

    A
    `(pi)/(2)`
    B
    `- (pi)/(2)`
    C
    `(3pi)/(2)`
    D
    None of these

  • the principal value of sin^(-1)(-sqrt3/2) is

    A
    `-2π/3`
    B
    `-π/3`
    C
    `4π/3`
    D
    `5π/3`

  • The principal value of "sin"^(-1)("sin"(3pi)/(5)) is

    A
    `(3pi)/(5)`
    B
    `(-3pi)/(5)`
    C
    `(2pi)/(5)`
    D
    None of these

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    Find the values of the following trigonometric function : sin (-(11 pi)/3) .

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