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# Sinusoidal

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A scientist records the motion of a particle.  A graph of that motion is shown below.

a) What is the period of one complete cycle?
b) What is the range of this function?
c) If the particle can survive for twenty complete cycles before deteriorating, determine the domain of the function.
d) Determine the equation of the axis.
e) Determine the amplitude.

May 13, 2022

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A scientist records the motion of a particle.  A graph of that motion is shown below.

Hello DumpDude!

a) What is the period of one complete cycle?

$$\color{blue}4\ units_t$$

b) What is the range of this function?

$$\color{blue}\{range-f(t)\}=\{\mathbb d\ |\ -1\leq d\leq 3\}\ [units_d]$$
c) If the particle can survive for twenty complete cycles  before deteriorating,

determine the domain of the function.

$$\color{blue}\mathbb D=\{t\ |\ 0\leq t\leq 80\}\ [units_t]$$
d) Determine the equation of the axis.

$$\color{blue}d=f(t)=2\ cos\ (\frac{\pi}{2} t)+1\ [units_d]$$
e) Determine the amplitude.

$$\color{blue}2\ units_d$$

!

May 13, 2022
edited by asinus  May 13, 2022