Find the period and amplitude of the function. y = 5cos2θ
The function y = 5cos(2θ) can be written as y = 5cos(2θ + 0).
The general form of the cosine function is y = Acos(Bx - C) + D, where A represents the amplitude, B represents the frequency (which is related to the period), C is a phase shift, and D is a vertical shift.
From this form, we can see that the amplitude of the function is A = 5.
The general form also indicates that the period of the cosine function is given by 2π/B. For y = 5cos(2θ), B = 2, so the period is 2π/2 = π.
Therefore, the amplitude of the function is 5 and the period is π.