Question

complete the sentence below. the amplitude of the graphs of the sine and cosine functions is and the period of each is (type exact answers, using $pi$ as needed.)

Explanation:

Step1: Recall amplitude definition

For the basic sine function $y = \sin(x)$ and cosine function $y=\cos(x)$, the amplitude is the absolute - value of the coefficient of the trigonometric function. Since for $y = \sin(x)$ and $y=\cos(x)$ the coefficient is 1, the amplitude $A = 1$.

Step2: Recall period definition

The period of a trigonometric function $y = a\sin(bx + c)+d$ or $y=a\cos(bx + c)+d$ is given by $T=\frac{2\pi}{|b|}$. For $y = \sin(x)$ and $y=\cos(x)$, $b = 1$, so the period $T = 2\pi$.

Answer:

1; $2\pi$