Using the function f(x)=3sin12θ 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 . (2 points)

Answer 1

A) The period of a sin function is calculated by T = 2π/b, where b is the coefficient of θ in the function. In this case, b = 12, so the period is T = 2π/12 = π/6. The amplitude of the function is the coefficient of sinθ, which is 3.

Therefore, the period of the function is π/6 and the amplitude is 3.

B) To rewrite the function to have the same amplitude but with a period of π, we need to adjust the coefficient of θ. We can do this by multiplying the function by 6/π:

f(x) = 3sin(12θ) * (6/π)
f(x) = 18/π sin(12θ)

Now, the function has a period of π and an amplitude of 18/π.