Question

which domain window settings would be appropriate if you wanted to graph the given function in radians for exactly two periods?
$f(x) = \cos(x)$
$\text{xmin} = 0\\ \text{xmax} = 2\pi$
$\text{xmin} = -180\\ \text{xmax} = 180$
$\text{xmin} = -\pi\\ \text{xmax} = 3\pi$
$\text{xmin} = 0\\ \text{xmax} = 720$

Explanation:

Step1: Identify period of $\cos(x)$

The period of $f(x)=\cos(x)$ is $2\pi$ radians.

Step2: Calculate total length for 2 periods

Total domain length = $2 \times 2\pi = 4\pi$

Step3: Evaluate each option

• Option1: $2\pi - 0 = 2\pi$ (1 period)
• Option2: Uses degrees, not radians (invalid)
• Option3: $3\pi - (-\pi) = 4\pi$ (2 periods, radians)
• Option4: Uses degrees, not radians (invalid)

Answer:

Xmin $= -\pi$ Xmax $= 3\pi$