Deck 28: Graphs of Other Trigonometric Functions

Question 1

Determine whether the function below is even,odd,or neither.​ $$y = \frac { 1 } { 7 } \tan x$$ ​

A)Even
B)Odd
C)Neither

Answer 1

Odd

Question 2

Consider the function given by​ $y=x-\cos x$ ​ Use a graphing utility to select the graph of the function.
​

A)​​
B)​
C)​
D)​​
E)​​

Answer 2

​​

Question 3

Select the graph of the function below.Include two full periods.​ $$y = 4 \csc \pi x$$ ​

A)​
B)​​
C)​
D)​
E)​

Answer 3

​

Question 4

Use a graphing utility to select the graph of the two equations in the same viewing window.Use the graphs to determine whether the expressions are equivalent.​ $\begin{array} { l } y _ { 1 } = 2 \sin x \csc x , \\y _ { 2 } = 2\end{array}$ ​

A)​ The expressions are equivalent except
Sinx = 0,y₁ is undefined.
B)​ The expressions are equivalent except when sinx = 0,y₁ is undefined.
C)​ The expressions are equivalent except when
Sinx = 0,y₁ is undefined.
D)​ The expressions are equivalent except when sinx = 0,y₁ is undefined.
E)​ The expressions are equivalent except when sinx = 0,y₁ is undefined.

Question 5

State the period of the function:​ $$y = \frac { 1 } { 8 } \cot \pi x$$ ​

A) $7 \pi$
B) $5 \pi$
C) $6 \pi$
D) $\frac { \pi } { 2 }$
E)1

Question 6

Determine whether the function below is even,odd,or neither.​ $$f ( x ) = 3 \sec x$$ ​

A)Neither
B)Odd
C)Even

Question 7

A plane flying at an altitude of a miles above a radar antenna will pass directly over the radar antenna (see figure).Let d be the ground distance from the antenna to the point directly under the plane and let x be the angle of elevation to the plane from the antenna. $$a = 8$$ . ​
(d is positive as the plane approaches the antenna. )
Write d as a function of x.​

A)d = 8 csc x
B)d = 8 cot x
C)d = 8 cos x
D)d = 8 tan x
E)d = 8 sin x

Question 8

Select the graph of the function below.Include two full periods.​ $$y = - 2 \sec 2 x + 2$$ ​

A)​
B)​
C)​
D)​
E)​

Question 9

State the period of the function:​ $$y = \frac { 1 } { 2 } \sec \frac { \pi x } { 5 }$$ ​

A)​14
B)10
C) $$\frac { \pi } { 5 }$$
D) $$10 \pi$$
E)12

Question 10

State the period of the function:​ $$y = - \csc 4 x$$ ​

A) $\frac { \pi } { 5 }$
B) $$\frac { \pi } { 2 }$$ ​
C) $$\frac { \pi } { 4 }$$ ​
D) $\frac { \pi } { 3 }$ ​
E) $\frac { \pi } { 6 }$ ​

Question 11

Select the graph of the function below.Include two full periods.​ $$y = 0.4 \csc \pi x$$ ​

A)​
B)​
C)​
D)​
E)​

Question 12

Consider the functions given by​ $$f ( x ) = 2 \sin x$$
$$and$$
$$g ( x ) = \frac { 1 } { 2 } \csc x$$ on the interval (0,π). Describe the behavior of each of the functions as x approaches π.
​

A)f approaches 2 and g approaches +∞.
B)f approaches 0 and g approaches +∞.
C)f approaches +∞ and g approaches 0.
D)f approaches 0 and g approaches $$\frac { 1 } { 2 }$$ .
E)f approaches 2 and g approaches $$\frac { 1 } { 2 }$$ .

Question 13

State the period of the function:​ $y = - 3 \sec \frac { \pi x } { 3 }$ ​

A)​ $\frac { \pi } { 3 }$
B)6
C)8
D) $6 \pi$
E)12

Question 14

State the period of the function:​ $$y = \sec 8 x$$ ​

A) $\frac { \pi } { 8 }$
B) $\frac { \pi } { 4 }$ ​
C) $\frac { \pi } { 6 }$ ​
D) $\frac { \pi } { 5 }$ ​
E) $\frac { \pi } { 7 }$ ​

Question 15

Select the graph of the function below.Include two full periods.​ $$y = 4 \tan ( x + \pi )$$ ​

A)​
B)​
C)​
D)​
E)​

Question 16

State the period of the function: ​​ $$y = \tan \frac { x } { 3 }$$ ​

A) $5 \pi$
B) $\frac { \pi } { 2 }$
C) $6 \pi$
D) $3 \pi$
E) $4 \pi$

Question 17

Use a graphing utility to select the graph of the function:​ $$y = \frac { 1 } { 4 } \sec \left( \frac { \pi x } { 2 } + \frac { \pi } { 2 } \right)$$ ​

A)​
B)​
C)​
D)​
E)​

Question 18

Select the graph of the function below.Include two full periods.​ $$y = \frac { 1 } { 3 } \sec \pi x$$ ​

A)​
B)​
C)​
D)​
E)​

Question 19

Use a graphing utility to select the graph of the function:​ $$y = 0.3 \tan \left( \frac { \pi x } { 4 } + \frac { \pi } { 4 } \right)$$ ​

A)​
B)​
C)​
D)​
E)​

Question 20

Select the graph of the function below.Include two full periods.​ $$y = \tan \frac { \pi x } { 6 }$$ ​

A)​
B)​
C)​
D)​
E)​

Question 21

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.​ $$g ( x ) = 3 e ^ { - \frac { x ^ { 2 } } { 2 } } \sin x$$ ​

A)​
B)​
C)​
D)​
E)​

Question 22

Describe the behavior of the function below as x approaches $$\frac { \pi } { 2 } ^ { + }$$ .​ $$f ( x ) = \tan x$$ ​

A)f → +∞ as x → $\frac { \pi } { 2 } ^ { + }$ .
B)f → 0 as x → $\frac { \pi } { 2 } ^ { + }$ .
C)f → -∞ as x → $\frac { \pi } { 2 } ^ { + }$ .
D)f → 1 as x → $\frac { \pi } { 2 } ^ { + }$ .
E)f → -1 as x → $\frac { \pi } { 2 } ^ { + }$ .

Question 23

Describe the behavior of the function below as x approaches zero.​ $$f ( x ) = \frac { | x | } { 3 } \sin x$$ ​

A)f → -∞ as x → 0.
B)f → -1 as x → 0.
C)f → 1 as x → 0.
D)f → +∞ as x → 0.
E)f → 0 as x → 0.

Question 24

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.​ $$f ( x ) = 7 \cdot 2 ^ { - \frac { x } { 4 } } \cos \pi x$$ ​

A)​
B)​
C)​
D)​
E)​

Question 25

The projected monthly sales (in thousands of units)of lawn mowers (a seasonal product)are modeled by​ $$S = 71 + 3 t - 40 \cos \left( \frac { \pi t } { 6 } \right)$$ ​ where t is the time (in months),with t = 1 corresponding to January.Select the graph of the sales function over 1 year.
​

A)​
B)​
C)​
D)​
E)​

Question 26

Describe the behavior of the function below as x approaches zero.​ $$f ( x ) = x \sin x$$ ​

A)f → 0 as x → 0.
B)f → -1 as x → 0.
C)f → 1 as x → 0.
D)f → -∞ as x → 0.
E)f → +∞ as x → 0.

Question 27

Use a graphing utility to select the graph of the function​ $$y = \frac { 6 } { x } + \cos x , x > 0$$ ​ ​

A)​
B)​
C)​
D)​
E) ​

Question 28

Determine whether the function below is even,odd,or neither.​ $$f ( x ) = \frac { x } { 4 } + \tan ( x )$$ ​

A)Neither
B)Even
C)Odd

Question 29

Describe the behavior of the function below as x approaches π^-.​ $$f ( x ) = 2 \cot x$$ ​

A)f → -∞ as x → π^-.
B)f → +∞ as x → π^-.
C)f → 1 as x → π^-.
D)f → 0 as x → π^-.
E)f → -1 as x → π^-.

Question 30

Determine whether the function below is even,odd,or neither. ​​ $$f ( x ) = 4 \csc \frac { x } { 4 }$$ ​

A)Even
B)Odd
C)Neither

Question 31

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.​ $$f ( x ) = 3 e ^ { - x } \cos x$$ ​

A)​
B)​
C)​
D)​
E)​

Question 32

Describe the behavior of the function below as x approaches zero.​ $$f ( x ) = \frac { | x | } { 5 } \cos ( x )$$ ​

A)f → +∞ as x → 0.
B)f → 1 as x → 0.
C)f → 0 as x → 0.
D)f → -1 as x → 0.
E)f → -∞ as x → 0.

Question 33

A television camera is on a reviewing platform a meters from the street on which a parade will be passing from left to right (see figure).Write the distance d from the camera to a particular unit in the parade as a function of the angle x. a = 26.

A)d = 26tan x
B)d = 26sec x
C)d = 26cos x
D)d = 26cot x
E)d = 26sin x

Question 34

Describe the behavior of the function below as x approaches 0⁺.​ $$f ( x ) = 3 \cot x$$ ​

A)f → +∞ as x → 0⁺.
B)f → 0 as x → 0⁺.
C)f → -1 as x → 0⁺.
D)f → -∞ as x → 0⁺.
E)f → 1 as x → 0⁺.

Question 35

Describe the behavior of the function below as x approaches zero.​ $$f ( x ) = | 5 x \cos x |$$ ​

A)f → +∞ as x → 0.
B)f → 1 as x → 0.
C)f → 0 as x → 0.
D)f → -1 as x → 0.
E)f → -∞ as x → 0.

Question 36

Determine whether the function below is even,odd,or neither.​ $$f ( x ) = x ^ { 8 } \cot \frac { x } { 2 }$$ ​

A)Neither
B)Odd
C)Even

Question 37

Determine whether the function below is even,odd,or neither. ​
F(x)= 0.8 cot x
​

A)Neither
B)Even
C)Odd

Question 38

Determine whether the function below is even,odd,or neither.​ $$f ( x ) = \frac { x ^ { 2 } } { 3 } - 3 \sec x$$ ​

A)Even
B)Odd
C)Neither

Question 39

Describe the behavior of the function below as x approaches $- {\frac { \pi } { 2 }}^-$ .​ $f ( x ) = 4 \tan x$ ​

A)f → +∞ as x → $- {\frac { \pi } { 2 }}^-$ .
B)f → 0 as x → $- {\frac { \pi } { 2 }}^-$ .
C)f → 1 as x → $- {\frac { \pi } { 2 }}^-$ .
D)f → -∞ as x → $- {\frac { \pi } { 2 }}^-$ .
E)f → -1 as x → $- {\frac { \pi } { 2 }}^-$ .

Question 40

Determine whether the function below is even,odd,or neither.​ $$f ( x ) = x ^ { 3 } \csc \frac { x } { 5 }$$ ​

A)Neither
B)Odd
C)Even

Question 41

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound.​ $$f ( x ) = 2 ^ { - \frac { x } { 4 } } \cos x$$

A)​ As x → ∞,f(x)→ 0.
B)​ As x → ∞,f(x)→ 0.
C) As x → ∞,f(x)→ 0.
D)​ The function f(x)is unbounded as x → ∞.
E)​ The function f(x)is unbounded as x → ∞.

Question 42

Select the graph of the given function.Make sure to include at least two periods. $$y = - 3 \sec ( x + \pi )$$ ​

A)​
B)​
C)​
D)​
E)​

Question 43

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound.​ $$f ( x ) = 2 ^ { - x / 4 } \cos x$$ ​ ​

A)​ As x → ∞,f(x)→ ∞.
B)​ As x → ∞,f(x)→ ∞.
C)​ As x → ∞,f(x)→ 0.
D) As x → ∞,f(x)→ 0.
E)​ As x → ∞,f(x)→ ∞.

Question 44

Select the graph of the given function.Make sure to include at least two periods.​ $$y = \csc 2 x$$ ​

A)​
B) ​
C)​
D)​
E)

Question 45

Use a graphing utility to select the graph of the function below,making sure to show at least two periods.​ $$y = \sec \frac { x } { 2 }$$ ​​ ​ ​

Xscl = $$\frac { \pi } { 2 }$$ ​ ​
​​
Xscl = $\frac { \pi } { 2 }$ ​
​​
Xscl = $\frac { \pi } { 2 }$ ​
​
Xscl = $\frac { \pi } { 2 }$

A)​ ​​
B)​ ​
C)​ ​
D)​​ ​
E)​ ​

Question 46

Use a graphing utility to select the graph of the expression below,making sure to show at least two periods. ​​ $$y = \frac { 1 } { 2 } \csc \left( \frac { \pi x } { 3 } - \frac { \pi } { 3 } \right)$$ ​

A)
B)​
C)​
D)​
E)​

Question 47

An object weighing W pounds is suspended from the ceiling by a steel spring (see figure).The weight is pulled downward (positive direction)from its equilibrium position and released.The resulting motion of the weight is described by the function​ $y = \frac { 1 } { 2 } e ^ { - \frac { t } { 4 } } \cos 2 t , t > 0$ ​ where y is the distance (in feet)and t is the time (in seconds).
Use a graphing utility to select the graph of the function.
​​ ​

A)​
B)​
C)​
D)​
E)​

Question 48

Use the graph shown below to determine if the function is even,odd,or neither. ​​ $$y = \sin x$$ ​

A)Even
B)Odd
C)Neither

Question 49

Determine which of the graphs below represents ​​ $$y = | x \sin x |$$ ​

A)​
B)​
C)​
D)​
E)​

Question 50

Use a graphing utility to select the graph of the function below.Describe the behavior of the function as x approaches 0. ​​ $$f ( x ) = x \cos \frac { 1 } { x }$$

A)​ As x → 0,f(x)→ 0.
B)​ ​As x → 0,f(x)→ 0.
C)​ As x → 0,f(x)→ 0.
D)​ As x → 0,f(x)→ 0.
E)​ As x → 0,f(x)→ 0.

Question 51

Which of the following functions is represented by the graph below?

A)​ $y = \frac { 1 } { 3 } \csc \frac { \pi x } { 2 }$
B)​ $y = \frac { 1 } { 3 } \tan \frac { \pi x } { 2 }$
C)​ $y = \cot ( x + \pi )$
D)​ $y = \frac { 1 } { 3 } \csc \pi x$
E)​ $y = \sec \left( \frac { x } { 3 } \right)$