SOLUTION: Given the range of a sinusoidal function is {y|y ∈ R,−6 ≤ y ≤ 0}, determine the amplitude and the equation of the central axis. I NEED YOUR HELP ASAP! thanks

Algebra ->  Trigonometry-basics -> SOLUTION: Given the range of a sinusoidal function is {y|y ∈ R,−6 ≤ y ≤ 0}, determine the amplitude and the equation of the central axis. I NEED YOUR HELP ASAP! thanks      Log On


   

Question 1181062: Given the range of a sinusoidal function is {y|y ∈ R,−6 ≤ y ≤ 0}, determine the amplitude and the equation of the central axis.

I NEED YOUR HELP ASAP! thanks
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=Asin%28Bx%2BC%29%2BD
Where
A=Amplitude
2pi%2FB=Period
C%2FB=Phase shift
D=Vertical shift
Range=[D-A,A%2BD]
or
Range=[A%2BD,D-A]
{y|y ∈ R,-6 ≤ y ≤ 0}
D-A=-6
D=A-6............eq.1
A%2BD=0
A=-D ....eq.2
=>D=A-6=>D=-D-6=>2D=-6=>D=-3
=>A=-%28-3%29=3
Period of sine function is 2pi
2pi%2FB=2pi=>B=1
Phase shift
C%2FB=0%2F1=>C=0
f%28x%29=3sin%28x%29-3
the equation of the central axis: y=-3