30 pts Find the equation of the graphs below Use cosine when

(30 pts) Find the equation of the graphs below. Use cosine when appropriate. Describe whether the graph is a vertical stretch/compression, reflection and/or vertical shift of sine or cosine: 2. Equation: Description: 2m- 275 Equation: Description: 175 25 30 Equation: Description: 20 10 12 24

Solution

1)
notice here that at t = 0, the function hits the midline
So, this is a sine function
max = 5 , min = 1

So, Amplitude, A = (5 - 1)/2 = 2
Midline, D = (5 + 1)/2 = 3

Period starts at 0 and ends at 2pi
So, B = period/2pi
= 2pi/2pi
B = 1

And since it starts exactly at the midline,
there is no horizontal shift at all
C = 0

Thus
using y = Asin[B(x - C)] + D
we have

y = 2sin(x) + 3 ----> ANS

--------------------------------------------------------------------

Here it starts at min when t = 0
This is a negative cos curve

max = 275
min = -25

So, A = (max - min)/2 ---> 150
D = (max + min)/2 ---> 125

Period = 2pi itself
So, B = 1

And no C

Thus y = Acos[B(x - C)] + D

y = -150cos(x) + 125 --> ANS

---------------------------------------------------------------------

Starts at max
So, positive cos graph

Max = 30
Min = 10

A = (max - min)/2 = 10
D = (max + min)/2 ---> 20

Period = 12
So, B = 2pi/12 = pi/6

And C = 0 as no phase shift

So, y = Acos[B(x - C)] + D

y = 10cos(pi*x/6) + 20 ---> ANS