determine the amplitude and period of the following function. then, graph the function. y = 6 cos 4πx the…

determine the amplitude and period of the following function. then, graph the function. y = 6 cos 4πx the amplitude is 6. (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 = 6 cos 4πx the amplitude is 6. (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 cosine function

For the function $y = A\cos(Bx)$, the period $T$ is given by $T=\frac{2\pi}{|B|}$.

Step2: Identify the value of B

In the function $y = 6\cos(4\pi x)$, $B = 4\pi$.

Step3: Calculate the period

Substitute $B = 4\pi$ into the period - formula: $T=\frac{2\pi}{|4\pi|}$. Since $|4\pi|=4\pi$, then $T=\frac{2\pi}{4\pi}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$