SOLUTION: Function 1: y=7sin(x+5) Function 2:y=7cos(5x-1) Part A: Find the amplitude, period, y-minimum and maximum, and phase shift for Function 1. Part B: Find the amplitude, peri

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Function 1: y=7sin(x+5) Function 2:y=7cos(5x-1) Part A: Find the amplitude, period, y-minimum and maximum, and phase shift for Function 1. Part B: Find the amplitude, peri      Log On


   

Question 1180527: Function 1: y=7sin(x+5)
Function 2:y=7cos(5x-1)
Part A: Find the amplitude, period, y-minimum and maximum, and phase shift for Function 1.
Part B: Find the amplitude, period, y-minimum and maximum, and phase shift for Function 2
Part C: write a sentence to compare and contrast the two functions
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Function 1:
y=7sin%28x%2B5%29

Function 2:
y=7cos%285x-1%29
in general: y=Acos%28Bx-C%29%2BD
the amplitude is A
B=2pi%2Af where f is the frequency
f=1%2Fperiod
the period is 2pi%2FB
the phase shift is C
the vertical shift is D


Part A: Find the amplitude, period, y-minimum and maximum, and phase shift for Function 1.
y=7sin%28x%2B5%29
the amplitude is A=7
B+=++1
the period is 2pi/1=2pi
max{ 7sin%28x+%2B+5%29 } = 7 at x+=+2pi%2An+%2B+pi%2F2+-+5 for integer n
min{ 7sin%28x+%2B+5%29 } = -7 at x+=+2pi%2An+%2B+%283pi%29%2F2+-+5 for integer+n
the phase shift is C=-5, 5 units to the left


Part B: Find the amplitude, period, y-minimum and maximum, and phase shift for Function 2
y=7cos%285x-1%29
y=7cos%285%28x-1%2F5%29%29
the amplitude is A=7
B+=+5
the period is 2pi%2FB=2pi%2F5
the phase shift is C=1%2F5, 1%2F5 units to the right
the vertical shift is D=0
max{ 7cos%285x+-+1%29 } = 7 at x+=+1%2F5+%2B%282pi%2An%29%2F5 for integer n
min{ 7+cos%285+x+-+1%29 } =+-7 at x+=+pi%2F5+%2B+1%2F5+%2B%282pi%2An%29%2F5+ for integer n

Part C: write a sentence to compare and contrast the two functions
Both functions have the same amplitude, y coordinate of max and min, and no vertical shift. Functions have different phase shift.
Function 1 has the phase shift C=-5, 5 units to the left, and Function 2 has the phase shift C=1%2F5, +1%2F5 units to the right