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math

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1) The hour hand on a clock has a length of 12 cm. Let the orgin be at the center of the clock.
a) Sketch the graph of the vertical position of the tip of the hour hand versus the angle through which the hand turns for a time period of 72h. Assume that the hour hand starts at 9.
C)How many cycles appear in the graph in part a)

I have no idea how to drraw this please guide me I really need your help:( Thanks!

  • math - ,

    call your horizontal axis the t axis (usually the x-axis)
    call your vertial axis the y axis

    Your graph should be a sine curve, where a complete sine curve fits into 12 hours.
    So label you t axis in hrs , with its end at 72
    Since 72/12 = 6 , you will have to draw 6 complete sine curves
    you want y = 0 when t = 9, plot that
    you want y = 6 when t = 10 , plot that
    you want y = 12 , when t = 12 , plot that, it will be your maximum point
    you want y = 6 when t= 2
    you want y = 0 when t = 3
    you want y = -6 when t = 4
    you want y = -12 , when t = 6, this is your minimum point.
    join you points with a smooth sine curve, and repeat to t = 72+9 or 81, for 6 complete cycles of the curve.

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