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Find the maximum and the minimum value...

Find the maximum and the minimum values of the following function over R.
(i) `sin^(2) X`
`(ii) 7 cos x -24 sin x + 5`
(iii) `3 sin x-4 cos x`
`(iv) 3 cos (4x -5) + 4`
`(v ) (sin x+ cos x)`
`(vi) 5 sin x + 12 cosx + 13`
`(vii) (3 sin^(2) x+ 4)`
`(ix) 5 sin x + 12 cos x -13`

Text Solution

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

  • 5 sin x + 4 cos x =3 rArr 4 sin x - 5 cos x=

    A
    4
    B
    `4sqrt(2)`
    C
    `3sqrt(2)`
    D
    `sqrt(2)`

  • The minimum value of sin 4x+ cos 4 x is

    A
    `sqrt(2)`
    B
    `1//sqrt(2)`
    C
    `-sqrt(2)`
    D
    none

  • The minimum value of 7 cos x- 24 sin x +5 is

    A
    30
    B
    `sqrt(2) `
    C
    `-20`
    D
    `-sqrt(2) `

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    Find the extreme values of the following function over R. (i) sin^(2) (60^(0) + x) + sin^(2) (60^(0) - x) (ii) cos (x+ (Pi)/(3) ) + 2sqrt(2) sin (x+ (pi)/(3))-3 (iii) 3 sin^(2) x+ 5 cos^(2) x (iv) cos 2 x+ cos^(2) x (v ) cos x cos ((2pi)/(3) + x) cos ((2pi)/(3)-x)

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