How do you write an equation of the cosine function with amplitude 3 and period 4π?

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How do you write an equation of the cosine function with amplitude 3 and period 4π?

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Answer 1 · 2018-05-28T13:02:25

$y = 3 cos (\frac{2 π}{4 π} x) = 3 cos (\frac{x}{2})$ $y = 3 cos({2pi}/{4pi} x) = 3 cos(x/2)$

Answer 2 · 2018-05-28T13:30:21

The general form for the cosine function is:

$y = A cos (B x + C) + D$ $y = Acos(Bx+C)+D$

The amplitude is: $| A |$ $|A|$

The period is: $P = \frac{2 π}{B}$ $P = (2pi)/B$

The phase shift is $ϕ = - \frac{C}{B}$ $phi=-C/B$

The vertical shift is D

Explanation:

Given:

The amplitude is 3:

$| A | = 3$ $|A| = 3$

The above implies that A could be either positive or negative but we always choose the positive value because the negative value introduces a phase shift:

$A = 3$ $A = 3$

Given:

The period is

$P = 4 π$ $P = 4pi$

$4 π = \frac{2 π}{B}$ $4pi = (2pi)/B$

$B = \frac{1}{2}$ $B = 1/2$

Nothing is said about the phase shift and the vertical shift, therefore, we shall assume that $C$ $C$ and $D$ $D$ are 0.

Substitute these values into the general form:

$y = 3 cos (\frac{1}{2} x)$ $y = 3cos(1/2x)$

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How do you write an equation of the cosine function with amplitude 3 and period 4π?

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