SOLUTION: please help me solve this problem: Which of the following equations has amplitude=-2 period=pi/4,phase shift=-pi/2? THIS ARE THE POSSIBLE ANSWERS: a)y=-2cos8(x-pi/2) b)y=-2cos

Algebra ->  Trigonometry-basics -> SOLUTION: please help me solve this problem: Which of the following equations has amplitude=-2 period=pi/4,phase shift=-pi/2? THIS ARE THE POSSIBLE ANSWERS: a)y=-2cos8(x-pi/2) b)y=-2cos      Log On


   

Question 241983: please help me solve this problem:
Which of the following equations has amplitude=-2 period=pi/4,phase shift=-pi/2?
THIS ARE THE POSSIBLE ANSWERS:
a)y=-2cos8(x-pi/2)
b)y=-2cos8(x+pi/2)
c)y=-2cos4(x+pi/2)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
A general form for sin and cos functions is:
y = C + A*sin(B(x - D))
or
y = C + A*cos(B(x - D))
where
abs%28A%29 = Amplitude. So A = 2 or -2.
B = 2pi/period
C = Vertical shift
D = Horizontal (or phase) shift

You are given the amplitude so you know A. You are given the period so we can figure out B:
B+=+%282pi%29%2F%28pi%2F4%29
B+=+8
You are not given a vertical shift so we will use 0 for C. And you are give the phase shift so D = pi%2F2.

So now we just find the equation that fits the A, B, C and D the we found above. It should be clear that equation (a) is correct.

(BTW: The -2 for A means that the amplitude is 2 and, because of the minus, the graph is reflected about the x-axis.)