Question 1

Which of the following best describes the domain of the cosine function $$y = \cos x$$?

Accepted Answer

$$\{x \mid x \in \mathbb{R}\}$$

Question 2

What is the range of the sine function $$y = \sin x$$?

Accepted Answer

$$[-1, 1]$$

Question 3

Which of the following statements is true about the symmetry of the cosine function?

Accepted Answer

The cosine function is an even function.

Question 4

At which $$x-$$values does the sine function $$y = \sin x$$ attain its maximum value?

Accepted Answer

$$x = \frac{\pi}{2} + 2\pi n$$, where $$n is an $$integer

Question 5

Which of the following is NOT an $$x-$$intercept of the cosine function $$y = \cos x$$?

Accepted Answer

$$x = 0$$

Question 6

The sine function $$y = \sin x is $$periodic. What is its period?

Accepted Answer

$$2\pi$$

Question 7

Which of the following best describes the $$y-$$intercept of the cosine function $$y = \cos x$$?

Accepted Answer

$$1$$

Question 8

At which $$x-$$values does the cosine function $$y = \cos x$$ attain its minimum value?

Accepted Answer

$$x = \pi + 2\pi n$$, where $$n is an $$integer

Question 9

Which property distinguishes the sine function from the cosine function?

Accepted Answer

The sine function is odd, while the cosine function is even.

Question 10

A Ferris wheel rotates such that the height $$h (in $$meters) of a passenger above the ground at time $$t (in $$seconds) is modeled by $$h(t) = 10 + 8\cos(\frac{\pi}{15} t). $$What is the maximum height the passenger reaches?

Accepted Answer

$$18$$ meters

Question 11

Which of the following is an $$x-$$intercept of the sine function $$y = \sin x$$?

Accepted Answer

$$x = 0$$

Question 12

If $$y = \sin x$$ and $$y = \cos x$$ are graphed on the same axes, which of the following statements is true?

Accepted Answer

$$y = \sin x$$ and $$y = \cos x$$ have the same amplitude and period.

Question 13

A sound wave can be modeled by $$y = \sin x. $$What is the minimum value of $$y$$?

Accepted Answer

$$-1$$

Question 14

Which of the following $$x-$$values is a minimum point for $$y = \sin x$$?

Accepted Answer

$$x = \frac{3\pi}{2}$$

Question 15

If $$y = \cos x$$ models the daylight hours in a city throughout the year, what does the period $$2\pi$$ represent in this context?

Accepted Answer

One full year cycle of daylight variation

Properties of Sine and Cosine Functions

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