Question

8. Find the period and amplitude of the function.

Y=5cos2theta

Period: pi, radians; amplitude: 2.5
Period pi, radians; amplitude: 5
Period 2pi, radians; amplitude 2.5
Period 2pi, radians; amplitude 5

If anyone knows the rest of the test that would be amazing for this 18 question test. Thanks!

Answer 1

The general equation of the cosine function is
y = a cos nθ
where a is the amplitude
And n = 2π/period

by comparing the general equation with the given equation which is
Y = 5 cos 2θ
∴ a = 5 and n = 2
∴ period = 2π/n = 2π/2 = π
∴ The amplitude = 5 and the period = π

So, the correct answer is the second option

Period pi, radians; amplitude: 5