Question

How do you graph and list the amplitude, period, phase shift for `y=-cos2x-5`?

Answer 1

Amplitude 1
Period: `\pi`
Shift down 5
increment: `pi/4`

Explanation:

The period of `cosx` is `0 to 2pi`, so I try to find the starting point and ending point.

Start: `2x = 0 to x = 0`
End: `2x = 2pi to x = pi`
Period: `End - Start to pi - 0 = pi`
Increment: `(Period) / 4 to pi/4`
`0, pi/4, pi/2, (3pi)/4, pi`
`-1cosx - 5`
1 is the Amplitude, Shift down 5 units
First graph is `cos(2x)`
graph{cos(2x) [-9.08, 10.92, -9.04, 0.96]}

Second graph is `-cos(2x)`
graph{-cos(2x) [-9.08, 10.92, -9.04, 0.96]}

Third graph is `-cos(2x) - 5`
graph{-cos(2x) - 5 [-9.08, 10.92, -9.04, 0.96]}