determine the amplitude and period of the following function. then, graph the function. y = sin 4x the…

determine the amplitude and period of the following function. then, graph the function. y = sin 4x the amplitude is 1. (simplify your answer.) the period is. (type an exact answer using π as needed. use integers or fractions for any numbers in the expression.)

determine the amplitude and period of the following function. then, graph the function. y = sin 4x the amplitude is 1. (simplify your answer.) the period is. (type an exact answer using π as needed. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Recall period - formula for sine function

The general form of a sine function is $y = A\sin(Bx - C)+D$, and its period is given by $T=\frac{2\pi}{|B|}$.

Step2: Identify the value of B

For the function $y=\sin(4x)$, we have $B = 4$.

Step3: Calculate the period

Substitute $B = 4$ into the period - formula $T=\frac{2\pi}{|B|}$. Since $|B|=4$, then $T=\frac{2\pi}{4}=\frac{\pi}{2}$.

Answer:

$\frac{\pi}{2}$