Sinusoidal Function help?

Yes because the cosine and sine functions are identical except for a phase angle

shift of 90º :   cos(θ) = sin(θ + 90º)

Compare the two functions:

   y = A sin(Bt – C)  +  D         and          y = A cos(Bt – C)  +  D

where "t" is the horizontal axis variable. Often this variable represents time.

A : varies the amplitude of each function in the same way

B : varies the frequency of each function in the same way

C : varies the phase shift of each function in the same way

D : varies the vertical shift of each entire function in the same way

Intuitive proof:  The first step is TRUE and each following step is TRUE after

doing the same thing to each side.

       since:        cos(kt) = sin(kt + 90º)   ...   multiply by A

                     Acos(kt) = Asin(kt + 90º)   ...   multiply "t" term by B

                         Acos(Bkt) = Asin(Bkt + 90º)   ...   subtract phase angle C

              Acos(Bkt – C) = Asin(Bkt + 90º – C)   ...   add vertical shift D

    Acos(Bkt – C)  +  D = Asin(Bkt + 90º – C)  +  D

   Note: The constant "k" contains the initial frequency information.

            "B" increases that frequency by a factor of "B"

            "A", "C", and "D" have NO effect on the frequency of the waveforms.