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A sine function has the following key features:

Frequency = 1/6π

Amplitude = 2

Midline: y = 3

y-intercept: (0, 3)

The function is not a reflection of its parent function over the x-axis.

 graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

 

 Jan 23, 2019
 #1
avatar+111357 
+1

We have this form

 

y = A sin (Bx + C ) + D

 

A = the amplitude =  2

 

B.....shows the number of periods in 2pi

 

The frequency  =  1/6pi   =  1 / period......so the period is 6pi

To find  "B"   we have      2pi / [ 6 pi ]  =  (1/3)

 

C = the phase shift..there is none....so "C" = 0

 

D = the shift up/down.....the normal y intercept  for the sine is (0, 0)....so....the shift up  = 3 units....sice the y intercept = (0, 3)

 

So....the function is

 

y = 2sin (x/3) + 3

 

Here is the graph :   https://www.desmos.com/calculator/tlcanknjtl

 

 

cool cool cool

 Jan 23, 2019

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