Question 1

Which of the following best describes the domain of the function $$y = 	an x$$?

Accepted Answer

All real numbers except odd multiples of $$\frac{\pi}{2}$$

Question 2

What is the period of the function $$y = \cot x$$?

Accepted Answer

$$\pi$$

Question 3

Which of the following statements about the graph of $$y = 	an x is $$TRUE?

Accepted Answer

It has vertical asymptotes at odd multiples of $$\frac{\pi}{2}$$

Question 4

The range of $$y = \csc x is$$:

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 5

Which transformation occurs when graphing $$y = 2 	an(x - \frac{\pi}{4})$$ compared to $$y = 	an x$$?

Accepted Answer

Vertical stretch by 2 and shift right by $$\frac{\pi}{4}$$

Question 6

A real-world application: The angle of elevation $$x (in $$radians) to the top of a building is measured from a point $$d$$ meters away. If the height $$h of $$the building is given by $$h = d 	an x$$, what happens to $$h as$$ $$x$$ approaches $$\frac{\pi}{2}$$?

Accepted Answer

$$h$$ approaches infinity

Question 7

Which of the following is the correct equation for the vertical asymptotes of $$y = \sec x$$?

Accepted Answer

$$x = (2n+1)\frac{\pi}{2}$$, where $$n is an $$integer

Question 8

Given $$y = -\cot(2x)$$, what is the period of the function?

Accepted Answer

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

Question 9

Which of the following best describes the symmetry of the tangent and cotangent functions?

Accepted Answer

Both are odd functions

Question 10

If $$y = \csc x is $$undefined at $$x = n\pi$$, what is the value of $$n$$ for $$x = 0$$?

Accepted Answer

$$n = 0$$

Question 11

Which of the following is the correct range for $$y = \sec x$$?

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 12

A sound wave can be modeled by $$y = 3 	an(2x). $$What is the period of this wave?

Accepted Answer

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

Question 13

Which of the following is NOT a characteristic of the graph of $$y = \cot x$$?

Accepted Answer

Range of $$[-1, 1]$$

Question 14

If $$y = \sec x$$ and $$y = \cos x$$ are graphed together, what is true about their intersection points?

Accepted Answer

They intersect where $$\cos x = 1 or$$ $$\cos x = -1$$

Question 15

Which of the following best describes the domain of $$y = \csc x$$?

Accepted Answer

All real numbers except integral multiples of $$\pi$$

Question 16

A Ferris wheel rotates such that the height $$h (in $$meters) of a seat above the ground at time $$t (in $$seconds) is modeled by $$h = 10 \sec(\frac{\pi}{6} t). $$What is the period of the motion?

Accepted Answer

$$12$$

Question 17

Which of the following is the correct formula for the period of $$y = 	an(Bx)$$?

Accepted Answer

$$\frac{\pi}{B}$$

Question 18

If $$y = 2 \cot(x - \frac{\pi}{3})$$, what is the x-coordinate of the first vertical asymptote to the right of $$x = 0$$?

Accepted Answer

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

Question 19

Which of the following is true about the graph of $$y = 	an x$$?

Accepted Answer

It passes through the origin

Graphs of Other Trigonometric Functions

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