12 points Identify the amplitude period horizontal shift and

(12 points) Identify the amplitude, period, horizontal shift, and vertical shift. Then, sketch one complete cycle of the following. (If the function has no amplitude, vertical shift, or horizontal shift, say so. Also, include asymptotes in your graph.) 1. a. y 3 - 2co(2x- b. y =|cot(-x)

Solution

Solution:(a)

y = 3 - 2cos(2x - /3)

Use the form a*cos(bx - c) + d to find the variables used to find the amplitude, period, phase shift, and vertical shift.

y = - 2cos(2x - /3) + 3

a = -2 , b = 2 , c = /3 , d = 3

amplitude |a| = |-2| = 2

Period = 2 / |b| = 2 / |2| =

Phase Shift = c / b = (/3) / 2 = /6

Vertical shift = d = 3

Solution:(b)

y = (1/4) cot(-x)

Use the form a*cot(bx - c) + d to find the variables used to find the amplitude, period, phase shift, and vertical shift.

a = 1/4 , b = -1, c = 0 , d = 0

Since the function cot does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude = None

Period = / |b| = / |-1| =

Phase Shift = c / b = (0) / (-1) = 0

Vertical shift = d = 0