Chapter 1.6, Problem 16E

(a)

To determine

To find: The appropriate viewing window for that display two complete periods of the function $y=\sin x$ .

Answer to Problem 16E

A possible viewing window for that display two complete periods of the function $y=\sin x$ is $\left[0,4\pi \right]$ by $\left[-4,4\right]$ .

Explanation of Solution

Given information: The given function is $y=\sin x$ .

It is known that the period of function $y=\sin x$ is $2\pi$ . To display two periods of the function, the length of the window should be $4\pi$ .

The appropriate window for x -axis should be $\left[0,4\pi \right]$ .

Therefore, the possible viewing window for that display two complete periods of the function $y=\sin x$ is $\left[0,4\pi \right]$ by $\left[-4,4\right]$ .

(b)

To determine

To find: The appropriate viewing window for that display two complete periods of the function $y=\cos x$ .

Answer to Problem 16E

A possible viewing window for that display two complete periods of the function $y=\cos x$ is $\left[0,4\pi \right]$ by $\left[-4,4\right]$ .

Explanation of Solution

Given information: The given function is $y=\cos x$ .

It is known that the period of function $y=\cos x$ is $2\pi$ . To display two periods of the function, the length of the window should be $4\pi$ .

The appropriate window for x -axis should be $\left[0,4\pi \right]$ .

Therefore, the possible viewing window for that display two complete periods of the function $y=\cos x$ is $\left[0,4\pi \right]$ by $\left[-4,4\right]$ .

(c)

To determine

To find: The appropriate viewing window for that display two complete periods of the function $y=\tan x$ .

Answer to Problem 16E

A possible viewing window for that display two complete periods of the function $y=\tan x$ is $\left[0,2\pi \right]$ by $\left[-3,3\right]$ .

Explanation of Solution

Given information: The given function is $y=\tan x$ .

It is known that the period of function $y=\tan x$ is $\pi$ . To display two periods of the function, the length of the window should be $2\pi$ .

The appropriate window for x -axis should be $\left[0,2\pi \right]$ .

Therefore, the possible viewing window for that display two complete periods of the function $y=\tan x$ is $\left[0,2\pi \right]$ by $\left[-3,3\right]$ .