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The sinusoidal function [tex]f(x) = 48 sin (6x-\frac{\pi }{9} )+48[/tex] models the height, in centimeters, that a valve stem of the a tire is above ground x seconds after the tire begins to rotate.

How long does it take the valve stem to complete one revolution?

Enter your answer, rounded to the nearest hundredth of a second, in the box.

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MathPhys

Answer:

1.05 s

Step-by-step explanation:

The generic form of a sinusoidal function is:

f(x) = A sin(2π/T x + B) + C

where A is the amplitude,

T is the period (time per revolution),

B is the horizontal offset (or phase shift),

and C is the vertical offset (or midline).

2π/T = 6

2π = 6T

T = π/3

T ≈ 1.05 s

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