Question

Write an equation of the cosine function with the given amplitude, period, phase shift, and vertical shift. amplitude: 2, period = , phase shift = – , vertical shift = –2

Answer 1

`y=2\cos(2x+(1)/(4))-2`

or

`y=-2\cos(2x+(1)/(4))-2`

Explanation:

`y=a cos(c(x-b))+d` has:

1) amplitude=|a|

2) phase shift=b

3) period=2pi/c

d) vertical shift=d

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You are given the amplitude is 2. This means a could either be 2 or -2.

You are given phase shift is -1/8. This means b is -1/8.

You are given the period is pi. So we need to solve pi=2pi/c.

pi=2pi/c

Dividing both sides by pi gives:

1=2/c

Multiply both sides by c gives:

c=2

The vertical shift is -2 so d=-2.

The equation could either be:

y=2cos(2(x-(-1/8)))-2

or

y=-2cos(2(x-(-1/8)))-2

Simplifying a little gives:

y=2cos(2x+1/4)-2

y=-2cos(2x+1/4)-2