557 The curve above is the graph of a sinusoidal function It

5.5.7

The curve above is the graph of a sinusoidal function. It goes through the point (6,3). Find a sinusoidal function that matches the given graph. If needed, you can enter pi = 3. 1416... as \'pi\' in your answer, otherwise use at least 3 decimal digits. f(x) =

Solution

1)period =2/B=12

=>B=2/12

=>B=/6

amplitude =A=3

phase shift =-C/B=6

=>-C/(/6) =6

=>C=-

comparing with y =Acos(Bx+C)

f(x)=3cos((/6)x- )

f(x)=-3cos((/6)x)