Question

How do you find the maximum of the graph `y=-2cos(x-pi/2)`?

Answer 1

`((3pi)/2, 2)`

Explanation:

The maximum and minimum of any `cos` graph on its own will be `+1` or `-1`. It doesn't matter so much what's inside the `cos` function, only what's outside.

Multiply these by `-2`, the outside of the equation, to get maximum/minimum points of `-2` and `+2`.

The maximum is therefore `+2`.

To find at which point this occurs, work backwards.

`+2 = -2cos(x-pi/2)`

Divide both sides by `-2`

`-1 = cos(x-pi/2)`

Do a backwards `cos` (`cos^-1`) to get rid of the forwards `cos`

`cos^-1(-1)=x-pi/2`
`pi = x-pi/2`
`x = (3pi)/2`

Now we have our `x` and `y` values:

`((3pi)/2, 2)`