Question

Which cosine function has maximum of 2, a minimum of –2, and a period of 2pi/3 ?

Answer 1

Given:

maximum = 2, minimum = -2

period = 2π/3

Find: the cosine function having those attributes stated above

Solution:

Cosine equations follow the pattern below:

`y=Acos(B(x-C))+D`

where A = amplitude, B = 2π/period, C = horizontal shift, and D = vertical shift.

Since the only given information is the period, let's calculate for the value of B.

`B=(2\pi)/(period)\Rightarrow B=(2\pi)/((2\pi)/(3))=3`

Out of the choices, only y = 2cos 3θ has the value of B which is 3. Hence, y = 2cos 3θ is the cosine function that has a maximum of 2, a minimum of –2, and a period of 2pi/3. (Option 3)