Math (Pre-calc)

I need to know how to solve this for my review questions. Thanks!

The wheel on a racing bike have a radius of 14 in. How fast is the cyclist traveling in mph if the wheels are turning at 280 revolutions per minute.

find the exact value of the expression.

Sin(2pi/3)+ tan(3pi/4)

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asked by matt
  1. 1 rotation = 2π(14) or 28π inches
    In 1 minute he goes 280(28π) inches
    = 7840π inches
    In 1 hour he goes 60(7840π) inches
    = 60(7840π)/12 feet
    = 60(7840π)/(12*5280) miles
    = appr 23.3 mph

    sin(2π/3)
    = sin 120°
    = sin 60°
    = √3/2 , from the standard 30°-60°-90° triangle

    tan(3π/4)
    = tan 135°
    = -tan 45°
    = -1

    your Sin(2pi/3)+ tan(3pi/4)
    = √3/2 - 1
    = (√3 - 2)/2

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    posted by Reiny

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