Solution: The height of the point begins at the lowest value, 0, increases to the highest value of 28 inches, and continues to oscillate above and below a center height of 14 inches. In terms of the angle of rotation, θ: h(θ) = 14 cos(θ) + 14 In this case, x is representing a linear distance the wheel has travelled, corresponding to an arclength along the circle. Since arclength and angle can be related by s = rθ, in this case we can write x = 14θ , which allows us to express the angle in terms of x: θ(x) = x/14 Substituting θ(x) in the above cosine function, we get: h(x) = h(θ(x)) = 14cos(x/14) + 14 = 14(cos((1/14)x) + 14 The period of this function would be P = 2π/B = 2π/(1/14) = 2π.14 = 28π , the circumference of the circle. This makes sense – the wheel completes one full revolution after the bicycle has travelled a distance equivalent to the circumference of the wheel.
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