Using the function f(x)=3sin12θ

Question

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 the function is given by the formula 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 given by the absolute value of the coefficient in front of sin(12θ), which is 3. Therefore, the amplitude is |3| = 3.

B)
To have the same amplitude but a period of π, we need to adjust the coefficient of θ. Since the original period is π/6, we need to multiply the coefficient by 6 to achieve the desired period of π. The original function is f(x) = 3sin12θ, so the adjusted function would be:

f(x) = 3sin(72θ).