Using the function f(x)=3sin12θ
𝑓
(
𝑥
)
=
3
sin
1
2
𝜃
A) What are the period and amplitude of the function? (2 points)
B) Rewrite the function to have the same amplitude, but with a a period of π
𝜋
. (2 points)
A)
The period of the function is given by T = 2π/12 = π/2 and the amplitude is 3.
B)
To have the same amplitude of 3 but with a period of π, we can adjust the function as follows:
f(x) = 3sin(12x(π/2))
f(x) = 3sin(6πx)
This function now has an amplitude of 3 and a period of π.