How do you find the amplitude, period, vertical and phase shift and graph #y=cos(theta-45)#?

1 Answer
Jul 5, 2017

First, you should rewrite the equation so it uses radians instead of degrees.
45° = #pi/4#

#y = cos (theta - pi/4)#

The standard form of a cosine function is #y=acos(bx + c) + d#, where #a# is the amplitude, #c# is the horizontal shift, and #d# is the vertical shift.

In this equation,
#a = 1#, #b = 1#, #c = -pi/4#, #d = 0#

The period of a cosine (and sine) function is #(2pi)/abs(b)#.
#(2pi)/abs(b) = (2pi)/abs(1) = 2pi#

Thus, the amplitude is 1, the period is #2pi#, there is no vertical shift, and there is a phase shift of #pi/4# to the right.

graph{cos (x-pi/4) [-10, 10, -5, 5]}