Question

How do you use transformation to graph the cosine function and determine the amplitude and period of `y=-cos(x-pi/4)`?

Answer 1

One of the standard forms of a trig function is y = ACos(Bx + C) + D

Explanation:

A is the amplitude (absolute value since it's a distance)

B affects the period via formula Period = `{2\pi}/B`

C is the phase shift

D is the vertical shift

In your case, A = -1, B = 1, C = `-\pi/4` D = 0

So, your amplitude is 1

Period = `{2\pi}/B->{2\pi}/1->2\pi`

Phase shift = `\pi/4` to the RIGHT (not the left as you might think)

Vertical shift = 0