y = A sin (Bx)
Period: starts at 0 and restarts at 4π
Period = 4π
Period = [tex]\frac{2\pi}{B}[/tex]
4π = [tex]\frac{2\pi}{B}[/tex]
B = [tex]\frac{2\pi}{4\pi}[/tex]
B = [tex]\frac{1}{2}[/tex]
A = amplitude. The minimum is -3 and the maximum is +3.
A = [tex]\frac{3 - (-3)}{2}[/tex]
A = [tex]\frac{6}{2}[/tex]
A = 3
y = A sin (Bx)
↓ ↓
y = 3 sin ([tex]\frac{1}{2}x[/tex])
*******************************************************
sin is an odd function so f(x) = -f(x)
Answer: y = [tex]-\frac{1}{2}[/tex] (sin 2πx)
form is: y = A sin (Bx) ; where A is the amplitude so,
Amplitude (A) = ([tex]\frac{1}{2}[/tex])
The range is between -1/2 and +1/2 so,
Range = [[tex]-\frac{1}{2}[/tex] ,[tex]\frac{1}{2}[/tex]]
Period = [tex]\frac{2\pi}{B}[/tex]
Period = [tex]\frac{2\pi}{|-2\pi|}[/tex]
Period = 1
y = [tex]\frac{1}{2}[/tex] sin (-2πx)
x=0 ⇒ y = [tex]\frac{1}{2}[/tex] sin(-2π(0))
= [tex]\frac{1}{2}[/tex] sin(0)
= [tex]\frac{1}{2}[/tex] (0)
= 0
(0, 0) works!
x=[tex]\frac{\pi}{2}[/tex] ⇒ y = [tex]\frac{1}{2}[/tex] sin(-2π([tex]\frac{\pi}{2}[/tex]))
= [tex]\frac{1}{2}[/tex] sin(-π²)
= [tex]\frac{1}{2}[/tex] (0.17)
= 0.085
([tex]\frac{\pi}{2}[/tex], 1) does NOT work
see attachment for the rest of the points:
(π, 0) does NOT work
[tex](\frac{3\pi}{2}, -1)[/tex] does NOT work
(2π, 0) does NOT work
Graph: D
