Question 1

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

Accepted Answer

A) Even 
B) Odd 
C) Neither 
A) Even 
B) Odd 
C) Neither B

Question 2

Find the complement of the following angle. ​
14°
​

Accepted Answer

A) Complement: 242° 
B) Complement: 14° 
C) Complement: 76° 
D) Complement: 166° 
E) Complement: 77° 
A) Complement: 242° 
B) Complement: 14° 
C) Complement: 76° 
D) Complement: 166° 
E) Complement: 77° C

Question 3

If the sides of a rectangular solid are as shown, and $s = 4$ , determine the angle, $\theta$, between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

Accepted Answer

A) 21.91o 
B) 24.09o 
C) 17.21o 
D) 26.28o 
E) 19.86o 
A) 21.91o 
B) 24.09o 
C) 17.21o 
D) 26.28o 
E) 19.86o B

Question 4

Evaluate each function.Round your answers to four decimal places.  
Csc3 and $\tan \frac { 1 } { 5 }$

Accepted Answer

A) 7.0862 and 0.2027 
B) 7.1862 and 0.3027 
C) 7.2362 and 0.3527 
D) 7.1362 and 0.2527 
E) 7.2862 and 0.4027 
A) 7.0862 and 0.2027 
B) 7.1862 and 0.3027 
C) 7.2362 and 0.3527 
D) 7.1362 and 0.2527 
E) 7.2862 and 0.4027

Question 5

Find the length of the arc, S, on a circle of radius 6 meters intercepted by a central angle of 90°.Round to two decimal places.

Accepted Answer

A) S = 9.42 meters 
B) S = 12.57 meters 
C) S = 18.85 meters 
D) S = 6.28 meters 
E) S = 7.54 meters 
A) S = 9.42 meters 
B) S = 12.57 meters 
C) S = 18.85 meters 
D) S = 6.28 meters 
E) S = 7.54 meters

Question 6

In traveling across flat land, you notice a mountain directly in front of you.Its angle of elevation (to the peak) is 3.5°.After you drive $x = 23$ miles closer to the mountain, the angle of elevation is 9°.Approximate the height of the mountain.(Round your answer upto one decimal place.)

Accepted Answer

A) 10.3 mi 
B) 2.3 mi 
C) 4.3 mi 
D) 8.3 mi 
E) 6.3 mi 
A) 10.3 mi 
B) 2.3 mi 
C) 4.3 mi 
D) 8.3 mi 
E) 6.3 mi

Question 7

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

Accepted Answer

A) f $\rightarrow$ –$\infty$ as x $\rightarrow$ 0. 
B) f $\rightarrow$ –1 as x $\rightarrow$ 0. 
C) f $\rightarrow$ 1 as x $\rightarrow$ 0. 
D) f $\rightarrow$ +$\infty$ as x $\rightarrow$ 0. 
E) f $\rightarrow$ 0 as x $\rightarrow$ 0. 
A) f $\rightarrow$ –$\infty$ as x $\rightarrow$ 0. 
B) f $\rightarrow$ –1 as x $\rightarrow$ 0. 
C) f $\rightarrow$ 1 as x $\rightarrow$ 0. 
D) f $\rightarrow$ +$\infty$ as x $\rightarrow$ 0. 
E) f $\rightarrow$ 0 as x $\rightarrow$ 0.

Question 8

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

Accepted Answer

A) f $\rightarrow$ +$\infty$as x $\rightarrow$0+. 
B) f $\rightarrow$ 0 as x $\rightarrow$ 0+. 
C) f $\rightarrow$ –1 as x $\rightarrow$ 0+. 
D) f $\rightarrow$ –$\infty$ as x $\rightarrow$ 0+. 
E) f $\rightarrow$ 1 as x $\rightarrow$ 0+. 
A) f $\rightarrow$ +$\infty$as x $\rightarrow$0+. 
B) f $\rightarrow$ 0 as x $\rightarrow$ 0+. 
C) f $\rightarrow$ –1 as x $\rightarrow$ 0+. 
D) f $\rightarrow$ –$\infty$ as x $\rightarrow$ 0+. 
E) f $\rightarrow$ 1 as x $\rightarrow$ 0+.

Question 9

The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = \frac { 1 } { 4 } \cos ( 6 t )$ , where y is the displacement (in feet) and t is the time (in seconds).Find the displacements when $t = 5$ .(Round your answers to two decimal places.)

Accepted Answer

A)  $y ( 5 ) \approx 0.04$ foot 
B)  $y ( 5 ) \approx 0.14$ foot 
C)  $y ( 5 ) \approx 0.44$ foot 
D)  $y ( 5 ) \approx 0.34$ foot 
E)  $y ( 5 ) \approx 0.24$ foot 
A)  $y ( 5 ) \approx 0.04$ foot 
B)  $y ( 5 ) \approx 0.14$ foot 
C)  $y ( 5 ) \approx 0.44$ foot 
D)  $y ( 5 ) \approx 0.34$ foot 
E)  $y ( 5 ) \approx 0.24$ foot

Question 10

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

Accepted Answer

A)    
B)    
C)    
D)     
E)    
A)    
B)    
C)    
D)     
E)

Question 11

Find angle $\frac { 3 \pi } { 2 }$ in degree measure.

Accepted Answer

A) 270° 
B) 275° 
C) 145° 
D) 135° 
E) 245° 
A) 270° 
B) 275° 
C) 145° 
D) 135° 
E) 245°

Question 12

Use an inverse trigonometric function to write $\theta$as a function of x.      
A = 5x
B = x + 9

Accepted Answer

A)  $\theta = \arctan \frac { x + 9 } { 5 x }$ 
B)  $\theta = \arcsin \frac { x + 9 } { 5 x }$ 
C)  $\theta = \operatorname { arcsec } \frac { x + 9 } { 5 x }$ 
D)  $\theta = \operatorname { arccsc } \frac { x + 9 } { 5 x }$ 
E)  $\theta = \arccos \frac { x + 9 } { 5 x }$ 
A)  $\theta = \arctan \frac { x + 9 } { 5 x }$ 
B)  $\theta = \arcsin \frac { x + 9 } { 5 x }$ 
C)  $\theta = \operatorname { arcsec } \frac { x + 9 } { 5 x }$ 
D)  $\theta = \operatorname { arccsc } \frac { x + 9 } { 5 x }$ 
E)  $\theta = \arccos \frac { x + 9 } { 5 x }$

Question 13

Evaluate (if possible) the sine, cosine, and tangent of the real number.   $t = \frac { 25 \pi } { 3 }$

Accepted Answer

A)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = - \sqrt { 3 }
\end{array}$ 
B)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { 1 } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = \sqrt { 3 }
\end{array}$ 
C)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
D)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
E) Not possible 
A)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = - \sqrt { 3 }
\end{array}$ 
B)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { 1 } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = \sqrt { 3 }
\end{array}$ 
C)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
D)  $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } 
\sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \
\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \
\tan \left( \frac { 25 \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 3 }
\end{array}$ 
E) Not possible

Question 14

Use the properties of inverse trigonometric functions to evaluate $\tan [ \arctan ( - 0.11 ) ]$ .

Accepted Answer

A)  $- 0.55$ 
B)  $0.12$ 
C)  $- 0.41$ 
D)  $- 0.11$ 
E)  $- 0.07$ 
A)  $- 0.55$ 
B)  $0.12$ 
C)  $- 0.41$ 
D)  $- 0.11$ 
E)  $- 0.07$

Question 15

Use a compass to sketch a quarter of a circle of radius 10 centimeters.Using a protractor, construct an angle of $a = 10 ^ { \circ }$ in standard position (see figure).Drop a perpendicular line from the point of intersection of the terminal side of the angle and the arc of the circle.By actual measurement, calculate the coordinates $$( x , y )$$ of the point of intersection and use these measurements to approximate the six trigonometric functions of a $$\text { "a" }$$ angle.(Round your answer to two decimal places.)

Accepted Answer

A) sin10° $\approx$  0.98, cos10° $\approx$  0.17, tan10° $\approx$  5.76,csc10° $\approx$ 0.18, sec10°$\approx$  1.02, cot10° $\approx$  5.67 
B) sin10° $\approx$  5.67, cos10°$\approx$  1.02, tan10° $\approx$  5.76,csc10° $\approx$  0.18, sec10° $\approx$  0.98, cot10° $\approx$  5.67 
C) sin10° $\approx$  0.17, cos10° $\approx$  0.98, tan10° $\approx$  0.18,csc10° $\approx$  5.76, sec10° $\approx$  1.02, cot10° $\approx$  5.67 
D) sin10° $\approx$  0.18, cos10° $\approx$  0.98, tan10° $\approx$  0.17,csc10° $\approx$ 10, sec10° $\approx$   0.98, cot10° $\approx$  5.76 
E) sin10° $\approx$  0.17, cos10° $\approx$  0.98, tan10° $\approx$  0.18,csc10° $\approx$  5.76, sec10° $\approx$  5.67, cot10° $\approx$  1.02 
A) sin10° $\approx$  0.98, cos10° $\approx$  0.17, tan10° $\approx$  5.76,csc10° $\approx$ 0.18, sec10°$\approx$  1.02, cot10° $\approx$  5.67 
B) sin10° $\approx$  5.67, cos10°$\approx$  1.02, tan10° $\approx$  5.76,csc10° $\approx$  0.18, sec10° $\approx$  0.98, cot10° $\approx$  5.67 
C) sin10° $\approx$  0.17, cos10° $\approx$  0.98, tan10° $\approx$  0.18,csc10° $\approx$  5.76, sec10° $\approx$  1.02, cot10° $\approx$  5.67 
D) sin10° $\approx$  0.18, cos10° $\approx$  0.98, tan10° $\approx$  0.17,csc10° $\approx$ 10, sec10° $\approx$   0.98, cot10° $\approx$  5.76 
E) sin10° $\approx$  0.17, cos10° $\approx$  0.98, tan10° $\approx$  0.18,csc10° $\approx$  5.76, sec10° $\approx$  5.67, cot10° $\approx$  1.02

Question 16

A granular substance such as sand naturally settles into a cone-shaped pile when poured from a small aperture.Its height depends on the humidity and adhesion between granules.The angle of elevation of a pile, θ, is called the angle of repose.If the height of a pile of sand is 11 feet and its diameter is approximately 34 feet, determine the angle of repose.Round answer to nearest degree.

Accepted Answer

A) 29o 
B) 30o 
C) 31o 
D) 32o 
E) 33o 
A) 29o 
B) 30o 
C) 31o 
D) 32o 
E) 33o

Question 17

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which d = 0.  
  $d = \frac { 1 } { 64 } \sin 794 \pi t$

Accepted Answer

A)  $64$ 
B)  $\frac { 1 } { 794 }$ 
C)  $794$ 
D)  $\frac { 1 } { 64 }$ 
E)  $\frac { 1 } { 1,584 }$ 
A)  $64$ 
B)  $\frac { 1 } { 794 }$ 
C)  $794$ 
D)  $\frac { 1 } { 64 }$ 
E)  $\frac { 1 } { 1,584 }$

Question 18

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which d = 0.   $d = \frac { 1 } { 12 } \sin 14 \pi t$

Accepted Answer

A)  $\frac { 1 } { 14 }$ 
B)  $\frac { 1 } { 12 }$ 
C)  $12$ 
D)  $\frac { 1 } { 6 }$ 
E)  $14$ 
A)  $\frac { 1 } { 14 }$ 
B)  $\frac { 1 } { 12 }$ 
C)  $12$ 
D)  $\frac { 1 } { 6 }$ 
E)  $14$

Question 19

Use the value of the trigonometric function to find $\sec ( - t )$ .   $\cos t = - \frac { 3 } { 4 }$

Accepted Answer

A)  $\sec ( - t ) = \frac { 4 } { 3 }$ 
B)  $\sec ( - t ) = - \frac { 3 } { 4 }$ 
C)  $\sec ( - t ) = - \frac { 4 } { 3 }$ 
D)  $\sec ( - t ) = \infty$ 
E)  $\sec ( - t ) = \frac { 3 } { 4 }$ 
A)  $\sec ( - t ) = \frac { 4 } { 3 }$ 
B)  $\sec ( - t ) = - \frac { 3 } { 4 }$ 
C)  $\sec ( - t ) = - \frac { 4 } { 3 }$ 
D)  $\sec ( - t ) = \infty$ 
E)  $\sec ( - t ) = \frac { 3 } { 4 }$

Question 20

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

Accepted Answer

A)    
B)    
C)     
D)    
E)    
A)    
B)    
C)     
D)    
E)

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

Find the complement of the following angle. 14°

Evaluate each function.Round your answers to four decimal places. Csc3 and $\tan \frac { 1 } { 5 }$

Find the length of the arc, S, on a circle of radius 6 meters intercepted by a central angle of 90°.Round to two decimal places.

In traveling across flat land, you notice a mountain directly in front of you.Its angle of elevation (to the peak) is 3.5°.After you drive $x = 23$ miles closer to the mountain, the angle of elevation is 9°.Approximate the height of the mountain.(Round your answer upto one decimal place.)

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

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

The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = \frac { 1 } { 4 } \cos ( 6 t )$ , where y is the displacement (in feet) and t is the time (in seconds).Find the displacements when $t = 5$ .(Round your answers to two decimal places.)

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

Find angle $\frac { 3 \pi } { 2 }$ in degree measure.

Use an inverse trigonometric function to write $\theta$ as a function of x. $Use an inverse trigonometric function to write \theta as a function of x. A = 5x B = x + 9$ A = 5x B = x + 9

Evaluate (if possible) the sine, cosine, and tangent of the real number. $t = \frac { 25 \pi } { 3 }$

Use the properties of inverse trigonometric functions to evaluate $\tan [ \arctan ( - 0.11 ) ]$ .

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which d = 0. $d = \frac { 1 } { 64 } \sin 794 \pi t$

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which d = 0. $d = \frac { 1 } { 12 } \sin 14 \pi t$

Use the value of the trigonometric function to find $\sec ( - t )$ . $\cos t = - \frac { 3 } { 4 }$

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

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 4: Trigonometry

Determine whether the function below is even, odd, or neither. f(x)=4csc⁡x4f ( x ) = 4 \csc \frac { x } { 4 }f(x)=4csc4x​

Find the complement of the following angle. ​ 14° ​

If the sides of a rectangular solid are as shown, and s=4s = 4s=4 , determine the angle, θ\thetaθ , between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

Evaluate each function.Round your answers to four decimal places. Csc3 and tan⁡15\tan \frac { 1 } { 5 }tan51​

Find the length of the arc, S, on a circle of radius 6 meters intercepted by a central angle of 90°.Round to two decimal places.

In traveling across flat land, you notice a mountain directly in front of you.Its angle of elevation (to the peak) is 3.5°.After you drive x=23x = 23x=23 miles closer to the mountain, the angle of elevation is 9°.Approximate the height of the mountain.(Round your answer upto one decimal place.)

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

Describe the behavior of the function below as x approaches 0+. f(x)=3cot⁡xf ( x ) = 3 \cot xf(x)=3cotx

Select the graph of the function below.Include two full periods. y=0.4csc⁡πxy = 0.4 \csc \pi xy=0.4cscπx

Find angle 3π2\frac { 3 \pi } { 2 }23π​ in degree measure.

Use an inverse trigonometric function to write θ\thetaθ as a function of x. A = 5x B = x + 9

Evaluate (if possible) the sine, cosine, and tangent of the real number. t=25π3t = \frac { 25 \pi } { 3 }t=325π​

Use the properties of inverse trigonometric functions to evaluate tan⁡[arctan⁡(−0.11)]\tan [ \arctan ( - 0.11 ) ]tan[arctan(−0.11)] .

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which d = 0. d=164sin⁡794πtd = \frac { 1 } { 64 } \sin 794 \pi td=641​sin794πt

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which d = 0. d=112sin⁡14πtd = \frac { 1 } { 12 } \sin 14 \pi td=121​sin14πt

Use the value of the trigonometric function to find sec⁡(−t)\sec ( - t )sec(−t) . cos⁡t=−34\cos t = - \frac { 3 } { 4 }cost=−43​

Select the graph of the given function.Make sure to include at least two periods. y=csc⁡2xy = \csc 2 xy=csc2x

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

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

Find the complement of the following angle. 14°

Evaluate each function.Round your answers to four decimal places. Csc3 and $\tan \frac { 1 } { 5 }$

In traveling across flat land, you notice a mountain directly in front of you.Its angle of elevation (to the peak) is 3.5°.After you drive $x = 23$ miles closer to the mountain, the angle of elevation is 9°.Approximate the height of the mountain.(Round your answer upto one decimal place.)

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

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

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

Find angle $\frac { 3 \pi } { 2 }$ in degree measure.

Use an inverse trigonometric function to write $\theta$ as a function of x. $Use an inverse trigonometric function to write \theta as a function of x. A = 5x B = x + 9$ A = 5x B = x + 9

Evaluate (if possible) the sine, cosine, and tangent of the real number. $t = \frac { 25 \pi } { 3 }$

Use the properties of inverse trigonometric functions to evaluate $\tan [ \arctan ( - 0.11 ) ]$ .

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which d = 0. $d = \frac { 1 } { 64 } \sin 794 \pi t$

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which d = 0. $d = \frac { 1 } { 12 } \sin 14 \pi t$

Use the value of the trigonometric function to find $\sec ( - t )$ . $\cos t = - \frac { 3 } { 4 }$

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