Chapter 6.3, Problem 4CFU

To determine

To draw: The graphs for the sine function and the cosine function. Compare and contrast the two graphs.

Explanation of Solution

Given information: Math journal: Sine function and the cosine function

Calculation:

The graphs are identical but for the fact that the sine graph is the same as $\cos \left(x-\frac{\pi }{2}\right)$ . That is it is shifted to the right $\frac{\pi }{2}$ units.

That being said, the period for both is $2\pi$ .

The domain for both is $\left(-\infty ,\infty \right)$ .

The range for both is $\left(-1,1\right)$ .

The x -intercept for $y=\cos \left(x\right)$ will occur every $\frac{\pi }{2}+n\pi ,n=\text{integer}$ .

The x -intercept for $y=\sin x$ will occur every $n\pi$ .

The y -intercept for $\cos \left(x\right)\text{ is at}\left(0,1\right)\text{ and }\sin \left(x\right)\text{ at}\left(0,0\right)$