SOLUTION: For the following table of data, determine an equation of a sine function that satisfies the given data. Link to the table is here: https://gyazo.com/d24e09b2d67cedcde8e0ddbcb6

x  | -120° | -60° |  0°  | 60° | 120° | 180° | 240° |
-----------------------------------------------------
y  |   1.5 |   3  | 1.5  |  0  | 1.5  |  3   | 1.5  |    

This is the graph:



The equation is



where  |A| = amplitude = (maximum value - minimum value)/2 = (3-0)/2 = 3/2,

So we substitute 3/2 for A



The period = 360°/B = length of one cycle. The first cycle goes from
-120° to 120° which is 120°-(-120°) = 120°+120° = 240°

So 360°/B = 240°
     360° = 240°B
360°/240° = B
      3/2 = B

We substitute 3/2 for B:



The phase (horizontal) shift, as we can tell from the graph, is 120° LEFT,
so C/B is +120°. (+ if left, and - if right)

C/B = 120°
  C = 120°B
  C = 120°(3/2)
  C = 180°

We substitute 180° for C



Finally the vertical shift is D and we can see that the graph has a
vertical shift upward of 1.5, so we substitute 1.5 for D:



And since 1.5 = 3/2 we can just write 3/2 for 1.5 and all the
constants just happened to came out to be 3/2.

 

Edwin