SOLUTION: For the following table of data, determine an equation of a sine function that satisfies the given data. Link to the table: https://gyazo.com/3b862caef87635d7e6ed3c70c8b6459a

Algebra ->  Rational-functions -> SOLUTION: For the following table of data, determine an equation of a sine function that satisfies the given data. Link to the table: https://gyazo.com/3b862caef87635d7e6ed3c70c8b6459a      Log On


   

Question 1161037: For the following table of data, determine an equation of a sine function that satisfies the given data.
Link to the table: https://gyazo.com/3b862caef87635d7e6ed3c70c8b6459a
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The general sine function is

y+=+a%2Asin%28b%28x-c%29%29%2Bd

a is the amplitude
b determines or is determined by the period
c is the horizontal phase shift
d is the vertical shift (determines the center line)

Here are the data:
  -120  -60   0   60  120  180  240
    1.5   3  1.5   0  1.5   3   1.5

The values oscillate between 0 and 3 over an interval of 240 degrees. That immediately tells us...

d is 1.5 (the graph oscillates about the middle value of 1.5)
a is 1.5 (the values oscillate 1.5 either side of the middle value)
the period is 240 degrees; that means b is 360/240 = 3/2 or 1.5

The "start point" for the basic sine graph is when the function value is the center value and increasing. For this function, the function value is the center value of 1.5 and increasing at 120 degrees, so the phase shift c is 120.

We have all the parameters we need to write the equation:

y+=+1.5%2Asin%281.5%28x-120%29%29%2B1.5

Here is a graph, showing the sine function along with the constants representing the center line and minimum and maximum values.