The graph below is one halfcycle of a tine function Accurate

The graph below is one half-cycle of a tine function Accurately draw one cycle. What is the sinusoidal axis, C, of this sinusoid? What is the amplitude, A, of this sinusoid? What is the period of this sinusoid? What is B? What is the phase displacement, D of this sinusoid? Using sine, what is the particular equation of this sinusoid? Graph the function y = 1 + 4 cos 3(theta - 40 degree) below. Plot all the point accurately.

Solution

sinusoid axis , C = 20

Amplitude = 30 -20 = 10

vertical shift, = 20

half cycle period = 5 -3 = 2

period = 4

B = 2pi/4 = pi/2

y = 20 + 10sin(pi/2(x - C)

graph passes through : ( 4 , 20)

20 = 20 + 10sin(pi/2(4 - C) )

0 = sin(pi/2(4 - C) )

pi = pi/2(4 - D)

2 = 4 - D

D = 2

phase shift D =2

y = 20 + 10sin(pi/2(x - 2)