Find a formula for the trigonometric function in the figure below.?

g(theta) = -3*cos(pi*theta/5) + 3.

Hints:   it looks like a shifted  cosine graoh to me [ though sine is also possible..but i think harder ]

Don't forget to choose a Best Answer.... with explanations...

g(@) = A cos { K ( @ - B )  } +  C     

A =  amplitude     period = 2π / K    B = horiz. shift     C = vert  shift

Graph appears to have a vertical shift of 3  and  an amplitude of  3 [ since the line y = 3  looks like it divides the graph in 1/2 ...   amplitude = distance from "center line" to the peak or valley ... or  1/2 the distance from peak to trough ], and the low point on normal cosine graph would be at -1 , but here it strikes the x axis ... so we must have lifted the graph upwards by our vertical shift of 3.

The normal cosine peak would be on y axis, ours is 5 radians over to right,  so shifted rt means  B =  5   [ if shifted left  we would use   B = - number ] .

Finally  the graph from crest to trough is 5 units wide,  but that is only 1/2 a cosine graph,  so  actual period is  10 radians wide  ....

  so,  2π / K = 10     K = π/5

put them all in the equation and if you have a Graphing Calculator  you will get the same picture if you graph from 0 to 10 radians  ...

       y = 3 cos (  (π/5) ( x - 5 )  ) + 3

Note: there is more than one correct answer  using either  sine or  cosine   :)  !!