The graph of one complete perlod of a cosine curve is given

The graph of one complete perlod of a cosine curve is given. (a) Find the amplitude, period, and phase shift. amplitude 9 period -2 phase shift (b) Write an equation that represents the curve in the form y=acos k(x-b). Submit Answer Save Progress 18. 5/5 points I

Solution

Max = +9 and Min. = -9

So, Amplitude = 9

Half cycle = 3pi/4 - pi/4 = 2pi/4 = pi/2

So, complete period = 2*pi/2 = pi

phase shift: y = acos[k(x -b)]

k = 2pi/pi = 2 ; a= 9

y = 9cos[ 2(x -b)]. find b using opne coordinate (0, 9)

9 = 9cos[2( 0 -b)] ; 1 = cos(-2b)

0 = b ; b =0

phase shift =0

So, y = 9cos(2x)