Question 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)
A) The period of the function f(x)=3sin12θ is given by T=2π/12=π/6. So, the period is π/6.
The amplitude of the function is the absolute value of the coefficient of sin, which is 3. So, the amplitude is 3.
B) To have the same amplitude but with a period of π, we need to adjust the coefficient of θ in the function. Since the period of sin function is 2π, we need to multiply the coefficient of θ by 6 to make the period equal to π. So, the function becomes f(x)=3sin(72θ) to have the same amplitude but with a period of π.