determine the amplitude and period of the following function. then, graph the function. y = 7 cos πx the…
determine the amplitude and period of the following function. then, graph the function. y = 7 cos πx the amplitude is 7. (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 a cosine function of the form $y = A\cos(Bx)$, the period $T$ is given by $T=\frac{2\pi}{|B|}$.
Step2: Identify the value of B
In the function $y = 7\cos(\pi x)$, we have $B=\pi$.
Step3: Calculate the period
Substitute $B = \pi$ into the period - formula: $T=\frac{2\pi}{|\pi|}$. Since $|\pi|=\pi$, then $T = 2$.
Answer:
2