Question 1

Determine the quadrant in which the angle 3 , given in radians, lies.

Accepted Answer

A)  1 
B)  3 
C)  4 
D)  2 
A)  1 
B)  3 
C)  4 
D)  2 D

Question 2

Solve for $y$.

Accepted Answer

A)  $y = 2 \sqrt { 3 }$ 
B)  $y = \frac { 2 \sqrt { 2 } } { 3 }$ 
C)  $y = \frac { \sqrt { 3 } } { 2 }$ 
D)  $y = \frac { 2 } { \sqrt { 3 } }$ 
E)  $y = 2 \sqrt { 2 }$ 
A)  $y = 2 \sqrt { 3 }$ 
B)  $y = \frac { 2 \sqrt { 2 } } { 3 }$ 
C)  $y = \frac { \sqrt { 3 } } { 2 }$ 
D)  $y = \frac { 2 } { \sqrt { 3 } }$ 
E)  $y = 2 \sqrt { 2 }$ A

Question 3

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the $\begin{array}{ccc}
\text { Line } & \text { Quadrant } & \text { Evaluate: } \
2 x+y=0 & \text { IV } & \csc \theta
\end{array}$

Accepted Answer

A)  $\frac { \sqrt { 5 } } { 2 }$ 
B)  $- \frac { 2 } { \sqrt { 5 } }$ 
C)  $- \frac { \sqrt { 5 } } { 2 }$ 
D)  $\frac { 2 } { \sqrt { 5 } }$ 
E)  $- \frac { 2 } { 1 }$ 
A)  $\frac { \sqrt { 5 } } { 2 }$ 
B)  $- \frac { 2 } { \sqrt { 5 } }$ 
C)  $- \frac { \sqrt { 5 } } { 2 }$ 
D)  $\frac { 2 } { \sqrt { 5 } }$ 
E)  $- \frac { 2 } { 1 }$ C

Question 4

Determine the value of $x$.

Accepted Answer

A)  $\frac { 34 \sqrt { 3 } } { 3 }$ 
B)  $\frac { 1 } { 34 }$ 
C)  34 
D)  $\frac { \sqrt { 3 } } { 34 }$ 
E)  $\frac { 17 } { 60 }$ 
A)  $\frac { 34 \sqrt { 3 } } { 3 }$ 
B)  $\frac { 1 } { 34 }$ 
C)  34 
D)  $\frac { \sqrt { 3 } } { 34 }$ 
E)  $\frac { 17 } { 60 }$

Question 5

Downtown Sardis City is located due north of a straight segment of train track oriented in an east-west direction (see map below). A passenger on a train that is traveling from west to east notes that downtown Sardis City is visible at an angle $A = 36 ^ { \circ }$ to the left of the tracks. After traveling a distance $d = 10$ kilometers, the passenger notes that the angle to Sardis City is $B = 41.5 ^ { \circ }$. Estimate the distance from the track to downtown Sardis City. Round to the nearest kilometer.

Accepted Answer

A)  $43 \mathrm {~km}$ 
B)  $41 \mathrm {~km}$ 
C)  $44 \mathrm {~km}$ 
D)  $45 \mathrm {~km}$ 
E)  $46 \mathrm {~km}$ 
A)  $43 \mathrm {~km}$ 
B)  $41 \mathrm {~km}$ 
C)  $44 \mathrm {~km}$ 
D)  $45 \mathrm {~km}$ 
E)  $46 \mathrm {~km}$

Question 6

Find the reference angle $\theta ^ { \prime }$ for the given angle $\theta$.
$$\theta = - 343 ^ { \circ }$$

Accepted Answer

A)  $107 ^ { \circ }$ 
B)  $73 ^ { \circ }$ 
C)  $27 ^ { \circ }$ 
D)  $17 ^ { \circ }$ 
E)  $7 ^ { \circ }$ 
A)  $107 ^ { \circ }$ 
B)  $73 ^ { \circ }$ 
C)  $27 ^ { \circ }$ 
D)  $17 ^ { \circ }$ 
E)  $7 ^ { \circ }$

Question 7

Find the exact value of the expression below.
$$\sin ^ { - 1 } \left[ \sin \left( \frac { 7 \pi } { 2 } \right) \right]$$

Accepted Answer

A)  $\frac { 7 \pi } { 2 }$ 
B)  $- \pi$ 
C)  $- \frac { \pi } { 2 }$ 
D)  $\frac { \pi } { 2 }$ 
E)  $- \frac { 7 \pi } { 2 }$ 
A)  $\frac { 7 \pi } { 2 }$ 
B)  $- \pi$ 
C)  $- \frac { \pi } { 2 }$ 
D)  $\frac { \pi } { 2 }$ 
E)  $- \frac { 7 \pi } { 2 }$

Question 8

Find the cotangent (if it exists) of the real number $t = \frac { 5 \pi } { 4 }$.

Accepted Answer

A)  $- \frac { \sqrt { 2 } } { 2 }$ 
B)  1 
C)  $- 1$ 
D)  0 
E)  $\cot \left( \frac { 5 \pi } { 4 } \right)$ does not exist 
A)  $- \frac { \sqrt { 2 } } { 2 }$ 
B)  1 
C)  $- 1$ 
D)  0 
E)  $\cot \left( \frac { 5 \pi } { 4 } \right)$ does not exist

Question 9

Write an algebraic expression that is equivalent to $\tan ( \arccos 3 x )$.

Accepted Answer

A)  $\frac { 1 } { 3 x }$ 
B)  $\frac { \sqrt { 1 - 9 x ^ { 2 } } } { 3 x }$ 
C)  $\sqrt { 1 - 9 x ^ { 2 } }$ 
D)  $\frac { 1 } { \sqrt { 1 - 9 x ^ { 2 } } }$ 
E)  $3 x$ 
A)  $\frac { 1 } { 3 x }$ 
B)  $\frac { \sqrt { 1 - 9 x ^ { 2 } } } { 3 x }$ 
C)  $\sqrt { 1 - 9 x ^ { 2 } }$ 
D)  $\frac { 1 } { \sqrt { 1 - 9 x ^ { 2 } } }$ 
E)  $3 x$

Question 10

Evaluate the cosine of the angle without using a calculator. $30 ^ { \circ }$

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $- \frac { \sqrt { 2 } } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 2 }$ 
E)  0 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $- \frac { \sqrt { 2 } } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 2 }$ 
E)  0

Question 11

Evaluate the sine of the angle without using a calculator.
$150 ^ { \circ }$

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $- \frac { \sqrt { 2 } } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 2 }$ 
E)  0 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $- \frac { \sqrt { 2 } } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 2 }$ 
E)  0

Question 12

A certain satellite orbits 13,000 miles above Earth's surface (see figure). Find the angle of depression $\alpha$ from the satellite to the horizon. Assume the radius of the Earth is 4000 miles. Round your answer to the nearest hundredth of a degree.

Accepted Answer

A)  $13.61 ^ { \circ }$ 
B)  $17.92 ^ { \circ }$ 
C)  $72.08 ^ { \circ }$ 
D)  $76.39 ^ { \circ }$ 
E)  $13.24 ^ { \circ }$ 
A)  $13.61 ^ { \circ }$ 
B)  $17.92 ^ { \circ }$ 
C)  $72.08 ^ { \circ }$ 
D)  $76.39 ^ { \circ }$ 
E)  $13.24 ^ { \circ }$

Question 13

Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in degrees.
$$\theta = 290 ^ { \circ }$$

Accepted Answer

Answers may vary. On

Question 14

Determine the graph of $y = \frac { 1 } { 3 } \cos ( x )$.

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Determine the exact value of $\arctan ( - 1 )$.

Accepted Answer

A)  $\frac { \pi } { 4 }$ 
B)  $- \frac { \pi } { 2 }$ 
C)  $- \frac { \pi } { 4 }$ 
D)  0 
E)  $\frac { \pi } { 2 }$ 
A)  $\frac { \pi } { 4 }$ 
B)  $- \frac { \pi } { 2 }$ 
C)  $- \frac { \pi } { 4 }$ 
D)  0 
E)  $\frac { \pi } { 2 }$

Question 17

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)
$\sec 41.3 ^ { \circ }$

Accepted Answer

A)  $- 1.1156$ 
B)  $0.7513$ 
C)  $1.3311$ 
D)  $- 0.7671$ 
E)  $0.8785$ 
A)  $- 1.1156$ 
B)  $0.7513$ 
C)  $1.3311$ 
D)  $- 0.7671$ 
E)  $0.8785$

Question 18

Use a calculator to evaluate $\tan 78 ^ { \circ } 30 ^ { \prime }$. Round your answer to four decimal places.

Accepted Answer

A)  $4.9152$ 
B)  $4.8288$ 
C)  $- 0.2445$ 
D)  $- 0.0398$ 
E)  $2.3649$ 
A)  $4.9152$ 
B)  $4.8288$ 
C)  $- 0.2445$ 
D)  $- 0.0398$ 
E)  $2.3649$

Question 19

Determine two angles (one positive and one negative, in radian measure) coterminal to the angle $\frac { \pi } { 4 }$.

Accepted Answer

A)  $\frac { 5 \pi } { 4 } , - \frac { 7 \pi } { 4 }$ 
B)  $\frac { 17 \pi } { 4 } , - \frac { 11 \pi } { 4 }$ 
C)  $\frac { 5 \pi } { 4 } , - \frac { 19 \pi } { 4 }$ 
D)  $\frac { 13 \pi } { 4 } , - \frac { 11 \pi } { 4 }$ 
E)  $\frac { 17 \pi } { 4 } , - \frac { 7 \pi } { 4 }$ 
A)  $\frac { 5 \pi } { 4 } , - \frac { 7 \pi } { 4 }$ 
B)  $\frac { 17 \pi } { 4 } , - \frac { 11 \pi } { 4 }$ 
C)  $\frac { 5 \pi } { 4 } , - \frac { 19 \pi } { 4 }$ 
D)  $\frac { 13 \pi } { 4 } , - \frac { 11 \pi } { 4 }$ 
E)  $\frac { 17 \pi } { 4 } , - \frac { 7 \pi } { 4 }$

Question 20

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set to the correct angle mode.)
$$\sec \left( \frac { - 5 \pi } { 8 } \right)$$

Accepted Answer

A)  $1.0006$ 
B)  $- 1.0824$ 
C)  $1.2331$ 
D)  $- 2.6131$ 
E)  $0.4142$ 
A)  $1.0006$ 
B)  $- 1.0824$ 
C)  $1.2331$ 
D)  $- 2.6131$ 
E)  $0.4142$

Determine the quadrant in which the angle 3 , given in radians, lies.

Solve for $y$ .

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the Line Quadrant Evaluate: 2x+y=0 IV \theta

Determine the value of $x$ .

Find the reference angle $\theta ^ { \prime }$ for the given angle $\theta$ . $\theta = - 343 ^ { \circ }$

Find the exact value of the expression below. $\sin ^ { - 1 } \left[ \sin \left( \frac { 7 \pi } { 2 } \right) \right]$

Find the cotangent (if it exists) of the real number $t = \frac { 5 \pi } { 4 }$ .

Write an algebraic expression that is equivalent to $\tan ( \arccos 3 x )$ .

Evaluate the cosine of the angle without using a calculator. $30 ^ { \circ }$

Evaluate the sine of the angle without using a calculator. $150 ^ { \circ }$

Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in degrees. $\theta = 290 ^ { \circ }$

Determine the graph of $y = \frac { 1 } { 3 } \cos ( x )$ .

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

Determine the exact value of $\arctan ( - 1 )$ .

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) $\sec 41.3 ^ { \circ }$

Use a calculator to evaluate $\tan 78 ^ { \circ } 30 ^ { \prime }$ . Round your answer to four decimal places.

Determine two angles (one positive and one negative, in radian measure) coterminal to the angle $\frac { \pi } { 4 }$ .

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set to the correct angle mode.) $\sec \left( \frac { - 5 \pi } { 8 } \right)$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Exam 4: Trigonometric Functions

Determine the quadrant in which the angle 3 , given in radians, lies.

Solve for yyy .

The terminal side of θ\thetaθ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of θ\thetaθ by finding a point on the Line Quadrant Evaluate: 2x+y=0 IV \theta

Determine the value of xxx .

Find the reference angle θ′\theta ^ { \prime }θ′ for the given angle θ\thetaθ . θ=−343∘\theta = - 343 ^ { \circ }θ=−343∘

Find the exact value of the expression below. sin⁡−1[sin⁡(7π2)]\sin ^ { - 1 } \left[ \sin \left( \frac { 7 \pi } { 2 } \right) \right]sin−1[sin(27π​)]

Find the cotangent (if it exists) of the real number t=5π4t = \frac { 5 \pi } { 4 }t=45π​ .

Write an algebraic expression that is equivalent to tan⁡(arccos⁡3x)\tan ( \arccos 3 x )tan(arccos3x) .

Evaluate the cosine of the angle without using a calculator. 30∘30 ^ { \circ }30∘

Evaluate the sine of the angle without using a calculator. 150∘150 ^ { \circ }150∘

A certain satellite orbits 13,000 miles above Earth's surface (see figure). Find the angle of depression α\alphaα from the satellite to the horizon. Assume the radius of the Earth is 4000 miles. Round your answer to the nearest hundredth of a degree.

Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in degrees. θ=290∘\theta = 290 ^ { \circ }θ=290∘

Determine the graph of y=13cos⁡(x)y = \frac { 1 } { 3 } \cos ( x )y=31​cos(x) .

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

Determine the exact value of arctan⁡(−1)\arctan ( - 1 )arctan(−1) .

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) sec⁡41.3∘\sec 41.3 ^ { \circ }sec41.3∘

Use a calculator to evaluate tan⁡78∘30′\tan 78 ^ { \circ } 30 ^ { \prime }tan78∘30′ . Round your answer to four decimal places.

Determine two angles (one positive and one negative, in radian measure) coterminal to the angle π4\frac { \pi } { 4 }4π​ .

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set to the correct angle mode.) sec⁡(−5π8)\sec \left( \frac { - 5 \pi } { 8 } \right)sec(8−5π​)

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Solve for $y$ .

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the Line Quadrant Evaluate: 2x+y=0 IV \theta

Determine the value of $x$ .

Find the reference angle $\theta ^ { \prime }$ for the given angle $\theta$ . $\theta = - 343 ^ { \circ }$

Find the exact value of the expression below. $\sin ^ { - 1 } \left[ \sin \left( \frac { 7 \pi } { 2 } \right) \right]$

Find the cotangent (if it exists) of the real number $t = \frac { 5 \pi } { 4 }$ .

Write an algebraic expression that is equivalent to $\tan ( \arccos 3 x )$ .

Evaluate the cosine of the angle without using a calculator. $30 ^ { \circ }$

Evaluate the sine of the angle without using a calculator. $150 ^ { \circ }$

Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in degrees. $\theta = 290 ^ { \circ }$

Determine the graph of $y = \frac { 1 } { 3 } \cos ( x )$ .

Determine the exact value of $\arctan ( - 1 )$ .

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) $\sec 41.3 ^ { \circ }$

Use a calculator to evaluate $\tan 78 ^ { \circ } 30 ^ { \prime }$ . Round your answer to four decimal places.

Determine two angles (one positive and one negative, in radian measure) coterminal to the angle $\frac { \pi } { 4 }$ .

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set to the correct angle mode.) $\sec \left( \frac { - 5 \pi } { 8 } \right)$