For the function r(z) = -4 sin(2z) + 1, indicate the amplitude, period, and equation of the midline.

Answer 1

Amplitude = 4

Period = 2pi/2 = pi

Midline is y=1

Answer 2

y = Asin(Bz + C) + D is the general equation for a sinosoidal wave, a transformation, up, down, right, left, phase shift, compression or stretching of y=sinz

for y = -4(sin2z +0) +1

A=-4, B=2, C=0 D =1

where A = Amplitude = half of the range of y = (max-min)/2 min= -3, max = 5, average = (5+3)/2 = 8/2 = 4

A stretches or compresses the sine wave function

B where 2pi/B = 2pi/2 = pi = period 2pi/B = the period. B=1 is the standard sine function with period = 2pi, the bigger B the smaller the period. the smaller B the bigger the period

C = horizontal shift =0

D = vertical shift upward = 1

midline is y = midpoint between max & min = (5 and -3)/2 = 2/2,

y=1 is the equation of the midline