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Math

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I posted this question before but accidentally typed in the wrong values! Please help, I just need to know the basic formula my book didn't provide any examples.

For the function y = -2sin(x-(pi/3)) between x = 0 and x = 2pi : (6 marks)

For what value(s) of x does y have its maximum value?
For what value(s) of x does y have its minimum value?
For what value(s) of x does y=1?

  • Math - ,

    dy/dx = -2cos(x - π/3)
    at a max/min , dy/dx = 0
    -2cos(x-π/3) = 0
    cos(x-π/3) = 0
    I know that cos π/2 = 0 or cos 3π/2 = 0
    so x - π/3 = π/2 or x - π/3 = 3π/2
    x = 5π/6 or x = 11π/6 , (150° or 330°)

    when x = 5π/6 , y = -2sin(π/2) = -2
    when x = 11π/6 , y = -2sin(3π/2) = +2

    so the function has a maximum value of 2 when x = 11π/3
    and a minimum value of -2 when x = 5π/6

    when y = 1
    -2sin(x-π/3) = 1
    sin(x-π/3) = -1/2
    I know sin 210° = -1/2 and sin 330°=-1/2
    which is 7π/6 or 11π/6
    x-π/3 = 7π/6 or x-π/3=11π/6
    x = 3π/2 or x = 13π/6

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