Consider the function y 3cos 2x pi2 for 0 le x le pi Follo

Consider the function y = 3cos (2x - pi/2) for 0 le x le pi. Follow the steps below to obtain a sketch the graph of y. State the amplitude, period and phase shift in the graph of this function. Solve 3 cos (2x - pi/2) = 0 for 0 le x le pi to find the horizontal intercepts (x-intercepts) of the function.

Solution

(a)Use the form acos(bxc)+d to find the variables used to find the amplitude, period, phase shift, and vertical shift.

a=3

b=2

c=2

d=0

(1)amplitude (|a|).

Amplitude: 3

(2)

The period of the function can be calculated using 2/|b|.

Period: (2/|b|)

Replace b with 2 in the formula for period.

Period: (2/|2|)=

Period:

(3)

The phase shift of the function can be calculated from c/b.

Phase Shift: c/b

Replace the values of c and b in the equation for phase shift.

Phase Shift: ((/2)/2)

Phase Shift: (/4)

(b)x intercepts means points where the curve cuts the x-axis,,, i.e y=0

Hence, 3cos(2x-/2)=0

Therefore, on silving we get, x=/2 and x=

Hence the intercepts are (/2,0) & (,0).