Question

A wind turbine in West Texas with a 50-meter diameter has damage on the tip of one of

its 3 blades. Workers are on a platform that is 2 meters below the tip of the damaged
blade at its lowest point. In maintenance mode, the turbine is set to complete one full
rotation every ten minutes to allow computes to analyze the effect of the damage and help
workers identify any adjustments that need to be made after repairs. Generate a
trigonometric function using cosine that models the height above the platform (h) of the
damage on the tip of the turbine blade as a function of time (t). y = acos(b(x - c)) + d

Answer 1

Explanation:

The trigonometric function using cosine that models the height above the platform (h) of the damage on the tip of the turbine blade as a function of time (t) can be represented by:

h = acos[(2/50) (πt - π/2)] + 2

where:

a = amplitude = 1

b = period = 2π/B = 2π/(50/2) = π/25

c = phase shift = π/2

d = vertical shift = 2

So the final function is:

h = acos[(2/50) (πt - π/2)] + 2