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The height of a nail in a bicycle tire as it rotates around is periodic in nature. The radius of the tire is 20cm and at the current pedalling speed the tire rotates once every second.

a. Determine the equation of a sinusoidal function that models this situation assuming that the nail starts on the ground at time zero.

b. At what time(s) during the first two seconds is the nail at a height of 10cm?

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