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Pre Calculus 12

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The height h, in metres, above the ground of a car as a ferris wheel rotates can be modelled by the function h(t) = 18cos(πt/80) +19

what is the minimum height of a car?
do i like subtract 19 from 18 ?

what is the maximum height of a car?
do i add the 19 to 18?

how long does it take for the wheel to revolve once?

80s?

The question below is a different question..

The period in degrees of the graph y = cos4x is?

Is it 45 degrees? I don't get how to solve this?

  • Pre Calculus 12 - ,

    Just look at the trig part of the function, namely the
    cos(....)
    the min value of that is -1 and the maximum is +1
    so 18cos(..) has a min of -18 and a max of +19

    so -18 + 19 = 1 metre, ---> minimum height of car
    and +18 + 19 = 37 ----> maximum height of car

    for y = a cos kx
    the period is 2π/k or 360°/k

    your value of k is π/80 , you had πt/80 which is (π/80)t
    so the period is 2π /(π/80)
    = 2π(80/π) = 160

    So the period is 160 seconds , if t is defined in seconds

    for the 2nd question:
    y = cos 4x ----> compare with y = cos kx
    period = 2π/4 radians or 360°/4
    = π/2 radians or 90°

    Memorize: period = 2π/k or 360°/k

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