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

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Answer 1 · 2018-02-23T13:09:42

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

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