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# Cosine equation?

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How do I find the equation of a cosine function with a maximum of 3, a minimum of -3, and a period of 4?

Guest May 6, 2017
#1
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How do I find the equation of a cosine function with a maximum of 3, a minimum of -3, and a period of 4?

lets see

y=3cos b(x+c)

c can be any constant becasue you have not mentioned phase shift.

where period = 2pi/b

$$\frac{2\pi}{b}=4\\ \frac{\pi}{b}=2\\ b=\frac{\pi}{2}$$

so it is

$$y=3cos[\frac{\pi }{2}(x+c)]$$

check (here is your graph )

https://www.desmos.com/calculator/nuopbcsgsn

Melody  May 6, 2017
edited by Melody  May 6, 2017
#2
+93683
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This is what you must remember.

$$y=a*cos[b(x+c)]+d\\~\\ \text{a is the amplitude}\\ \text{d is the vertical shift}\\ \text{c is the horizontal, or phase, shift}\\ \text{and last but not least, the period is}\frac{2\pi}{b}\\ \text{The angle is in radians}\\$$

If you remember that then these questions become almost trivia.

Sine functions work the same way.

Melody  May 6, 2017