Sinusoidal functions (phase shift)

Question

A sine function has a maximum value of -5, a minimum value of -29, and consecutive minimum values when x= -π/5 and x= (4π)/15. Determine the phase shift

Answer 1

 

 

Minimum                                       Maximum                                                Minimum

 

_|_______________|_______________|________________|________________|_____

 

-pi/5             (-pi/5)+(pi/30)      (-pi/5)+(4pi/15)                                            4pi/15

                             2                      2   

                                                                   

                         -pi/12                     pi/30

               Shifted pi/12 to the left

 

for f(x)=sin x halfway between the minimum and the maximum would be 0pi. But for the information the problem gives us, halfway between the minimum and the maximum is -pi/12.

So this one has been shifted pi/12 to the left.

 

Let me know if you need further help with this one.  :-)