Question 1

Which of the following best describes the symmetry of the function $$f(x) = \sin x$$?

Accepted Answer

It is odd, symmetric about the origin.

Question 2

What is the period of the function $$f(x) = \cos x$$?

Accepted Answer

$$2\pi$$

Question 3

Given the transformation $$y = 3 \sin(x - \frac{\pi}{2}) + 2$$, what is the amplitude of the resulting sine wave?

Accepted Answer

$$3$$

Question 4

Which of the following is the correct range for the function $$f(x) = \cos x$$?

Accepted Answer

$$[-1, 1]$$

Question 5

A sound wave can be modeled by $$y = 2 \sin(4x). $$What is the period of this wave?

Accepted Answer

$$\frac{\pi}{2}$$

Question 6

If $$f(x) = \cos(x)$$, which of the following statements is true?

Accepted Answer

$$f(-x) = f(x)$$, so it is even.

Question 7

Which transformation shifts the graph of $$y = \sin x to $$the right by $$\frac{\pi}{3}$$ units?

Accepted Answer

$$y = \sin(x - \frac{\pi}{3})$$

Question 8

A Ferris wheel rotates such that the height of a passenger above the ground can be modeled by $$h(t) = 10 \cos(t) + 12. $$What is the maximum height reached?

Accepted Answer

$$22$$

Question 9

Which equation represents a cosine function with amplitude $$5$$, period $$\pi$$, and no phase shift?

Accepted Answer

$$y = 5 \cos(2x)$$

Question 10

Which of the following real-world phenomena is best modeled by a sine function?

Accepted Answer

The daily temperature variation over a year.

Question 11

Given $$y = -2 \sin(x)$$, which statement is true about its graph compared to $$y = \sin(x)$$?

Accepted Answer

It is reflected over the x-axis and has amplitude 2.

Question 12

What is the x-intercept of $$y = \sin x$$ between $$0$$ and $$2\pi$$?

Accepted Answer

$$x = 0, \pi, 2\pi$$

Question 13

If $$y = \cos(x)$$, what is the value of $$y$$ when $$x = \pi$$?

Accepted Answer

$$-1$$

Question 14

Which of the following describes the effect of the transformation $$y = \sin(x) + 3$$?

Accepted Answer

Vertical shift up by 3 units.

Question 15

A medical device records heartbeats as a periodic signal modeled by $$y = 0.5 \sin(2\pi t). $$What is the amplitude of the signal?

Accepted Answer

$$0.5$$

Question 16

Which of the following is true about the domain of $$f(x) = \sin x$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 17

If $$y = \cos(x + \frac{\pi}{2})$$, which function does this graph correspond to?

Accepted Answer

$$y = -\sin(x)$$

Question 18

Which of the following equations represents a sine function with a period of $$\frac{2\pi}{3}$$?

Accepted Answer

Question 19

Which of the following is the correct formula for a sine function with amplitude $$A$$, period $$T$$, phase shift $$\phi$$, and vertical shift $$D$$?

Accepted Answer

$$y = A \sin\left(\frac{2\pi}{T}x + \phi\right) + D$$

Graphing Sine and Cosine Functions: Attributes, Symmetry, and Transformations

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