determine the amplitude and period of the function. graph the function. y = - 3 cos 1/2x the amplitude is 3…

determine the amplitude and period of the function. graph the function. y = - 3 cos 1/2x the amplitude is 3. (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 function. graph the function. y = - 3 cos 1/2x the amplitude is 3. (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

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

Step2: Identify the value of B

For the function $y=-3\cos(\frac{1}{2}x)$, we have $B = \frac{1}{2}$.

Step3: Calculate the period

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

Answer:

$4\pi$