As a fan turns counterclockwise, a bug sits 10.6 inches from the center of rotat

Question

As a fan turns counterclockwise, a bug sits 10.6 inches from the center of rotation on one of its blades. The bug is at the 3 o'clock position on the fan when it begins to turn. If the fan makes less than one full rotation, determine the distance the bug has traveled along its arc from the 3 o'clock position when its final position is... ..8 inches to the right of the vertical diameter of the fan for the second time. 2-costa /no.6 inches Preview ....4 inches to the left of the vertical diameter of the fan for the first time. (cos-3.4/10.0)*10.6" inches Preview 4 inches to the left of the vertical diameter of the fan for the second time. (2pl-cos(-4/10) 10.6 Preview inches

Explanation / Answer

radius of rotation, r=10.6 in

distance from vertical diameter= x= 10.6cos,distance from horizontalal diameter= y=10.6sin

a)

x=3.8, second time means in fourth quadrant

=>10.6cos =3.8

=> =2-cos-1(3.8/10.6)

distance bug travelled =r

distance bug travelled =10.6(2-cos-1(3.8/10.6)) inches exactly

distance bug travelled =53.8378 inches approximately

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b)

x=-3.4, first time means in second quadrant

=>10.6cos =-3.4

=> =-cos-1(3.4/10.6)

distance bug travelled =r

distance bug travelled =10.6(-cos-1(3.4/10.6)) inches exactly

distance bug travelled =20.1116 inches approximately

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c)

x=-4, second time means in third quadrant

=>10.6cos =-4

=> =+cos-1(4/10.6)

distance bug travelled =r

distance bug travelled =10.6(+cos-1(4/10.6)) inches exactly

distance bug travelled =45.85 inches approximately

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