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Write an equation of the cosine function with the given amplitude, period, phase shift, and vertical shift. amplitude: 2, period = π, phase shift = (–1/8)π , vertical shift = –2

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Answer:


2*cos(2x+(\pi)/(4) )-2

Explanation:

Recall the trigonometric definitions for the geometrical characteristics given to you:

For a General Harmonic function of the type:
f(x)=A* cos(Bx+C)+D

we define:

|A| = Amplitude of the function

Period of the function =
(2\pi )/(B)

Phase shift =
-(C)/(B)

vertical shift = D

Therefore we can construct a function that includes the appropriate geometric characteristics requested by using:

A = 2

To find B we use the definition of period, and what value we want it to have:
(2\pi )/(B)=\pi \\(2\pi )/(\pi)=B\\B=2

To find C we use the definition of phase shift and the value we want it to have (also using the value for B we found in the step above):
-(C)/(B)=-(\pi)/(8) \\-(C)/(2)=-(\pi)/(8)\\C=(2* \pi)/(8) =(\pi )/(4)

and finally, D = -2

Therefore the function will look like:
2*cos(2x+(\pi)/(4) )-2

User Arturh
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