SOLUTION: What would 5 characteristics of this sinusoidal graph be? y = 5 sin [3(x-2)] - 1 This is what I've figured out; but I want to be sure that I am correct. Midline is at y=

Algebra ->  Graphs -> SOLUTION: What would 5 characteristics of this sinusoidal graph be? y = 5 sin [3(x-2)] - 1 This is what I've figured out; but I want to be sure that I am correct. Midline is at y=      Log On


   

Question 947646: What would 5 characteristics of this sinusoidal graph be?
y = 5 sin [3(x-2)] - 1
This is what I've figured out; but I want to be sure that I am correct.
Midline is at y=1
Amplitude=5
Maximum=1+5=6
Minimum=1-5=(-4)
And the period I have no idea what it is.



Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
A sinusoid is the name given to any curve that can be written in the form
y=Asin%28B%28x-C%29%29%2BD ................(A and B are positive).

|A| = amplitude
B = cycles from 0 to 2pi
period+=2pi%2FB
D+= vertical shift (or displacement)
C+= horizontal shift (sometimes called "phase shift" when B+=+1)

you have
y+=+5+sin+%283%28x-2%29%29-+1+
so,

|A| = 5 (amplitude)
B+=3+ (cycles from 0 to 2pi)
period+=2pi%2FB=2pi%2F3
D+=-1 vertical shift (or displacement 1 unit down)
C+=2 ( horizontal shift, 2 units left)

maxy+=+5+sin%283+%28x-2%29%29-1} = 4 at x+=+2%2Bpi%2F6%2B%282n%2Api%29%2F3 for integer n
min{ y+=+5+sin%283+%28x-2%29%29-1} =+-6 at x+=+2%2Bpi%2F2%2B%282n%2Api%29%2F3 for integer n