Question

Determine an equation of a cosine function, given the following info: Amplitude: 3 Period: 120 V.Shift: 6 The function has a maximum at 15?

Answer 1

Finally sorted out! See the explanation.

Explanation:

The max/min ( amplitude) of `cos(x)` is +1 and -1. So if you wish to increase this to `color(red)(+-3)` we have `y=color(red)(3)cos(3(x-15))`

'Shifting' the graph to the right so that `ul(color(red)("a"))` maximum (not 'the' maximum) is achieved by looking at the plot of `cos(x)` at the point `color(red)(x-15)` and plotting it at `x`. Hence the `y=3cos(3(color(red)(x-15)))` The consequence is that the whole graph has been 'shifted' to the right by 15

'Squashing the curve is achieved by looking at a point for `color(red)(3)x " using "cos(x)` and plotting it at `x`. Hence the `y=3cos(color(red)(3)(x-15))`