SOLUTION: Graph the function y=3.5 sin(5x-80°)+1.5 by applying transformation to f(x) = sin x. State the amplitude, period, phase shift, and vertical shift.

Algebra ->  Rational-functions -> SOLUTION: Graph the function y=3.5 sin(5x-80°)+1.5 by applying transformation to f(x) = sin x. State the amplitude, period, phase shift, and vertical shift.      Log On


   

Question 1140832: Graph the function y=3.5 sin(5x-80°)+1.5 by applying transformation to f(x) = sin x.
State the amplitude, period, phase shift, and vertical shift.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=3.5sin%285x-80%29%2B1.5
+graph%28+600%2C+600%2C+-7%2C+7%2C+-7%2C+7%2C+3.5sin%285x-80%29%2B1.5%29+

compare to
y=Asin%28+Bx%2B-C+%29%2BD

Amplitude: A+(absolute value)
Period: %282pi%29%2FB+
Phase Shift: -C%2FB
Vertical Shift:+D
so, you have:
Amplitude: ±3.5
Period:
periodicity of a%2Asin%28bx%2B-c+%29±d= %28sin_+base_+periodicity%29%2Fabs%28b%29

sin%28x%29+base periodicity is 360°
so, period=+360%2F5=+72°

Vertical Shift: the graph shifts up by+D=1.5
Phase Shift: -C%2FB=80%2F5=16°