Write as a single sine function

Question

Which of the following expressions can be written as a single sine function of the form Asin(Bt+θ)? More than one answer can be right.

a.) 3sin(2t) + 5cos(2t)

b.) cos(pit)

c.) 2sin(3t) + 3cos(2t)

d.) sin(2t) + tan(2t)

e.) cos(pit) - 5sin(pit)

Answer 1

You can easily graph these (on your graphing calculator or on desmos or another graphing utility) and look at the results to see which is a regular sinusoid.

Any curve that has a constant amplitude and regular period can be written as Asin(Bt+θ)