Question

Which cosine function has maximum of 2, a minimum of –2, and a period of Start Fraction 2 pi over 3 End Fraction?

A. y = 3 cos 2θ
B. y = 2 cos Start Fraction 2 theta over 3 End Fraction
C. y = 2 cos 3θ
D. y = 2 cos Start Fraction theta over 3 End Fraction

Answer 1

B. y = 2 cos Start Fraction 2 theta over 3 End Fraction

Answer 2

since cos(kx) has period 2π/k, we need 2π/k = 2π/3, so k = 3
so our function is
C. y = 2 cos 3θ

Answer 3

Correct! The correct cosine function is y = 2 cos 3θ. This function has a maximum of 2, a minimum of -2, and a period of 2π/3.