Question 1

Solve the problem.
-$\cot ^ { 2 } 90 ^ { \circ } - \sec 180 ^ { \circ }$

Accepted Answer

A)  $- 1$ 
B)  1 
C)  0 
D)  2 
A)  $- 1$ 
B)  1 
C)  0 
D)  2

Question 2

Use the fundamental identities to find the value of the trigonometric function.
-Find the complement of an angle whose measure is 33°21´.

Accepted Answer

A) 57°38´ 
B) 57°39´ 
C) 56°39´ 
D) 56°21´ 
A) 57°38´ 
B) 57°39´ 
C) 56°39´ 
D) 56°21´

Question 3

Evaluate the expression.
-AC

Accepted Answer

A)  $\mathrm { RT }$ 
B)  ST 
C)  Cannot be determined 
D)  $\mathrm { RS }$ 
A)  $\mathrm { RT }$ 
B)  ST 
C)  Cannot be determined 
D)  $\mathrm { RS }$

Question 4

Find the measure of each angle in the problem.
-Complementary angles with measures 3x and 6x - 18 degrees

Accepted Answer

A) 66° and 114° 
B) 12° and 78° 
C) 36° and 54° 
D) 38° and 52° 
A) 66° and 114° 
B) 12° and 78° 
C) 36° and 54° 
D) 38° and 52°

Question 5

Find the angle of least positive measure coterminal with the given angle.
-x and y

Accepted Answer

A)  $x = 12 ; y = 3$ 
B)  $x = 8 ; y = 2$ 
C)  $x = 17 ; y = \frac { 17 } { 4 }$ 
D)  $x = 10 ; y = \frac { 5 } { 2 }$ 
A)  $x = 12 ; y = 3$ 
B)  $x = 8 ; y = 2$ 
C)  $x = 17 ; y = \frac { 17 } { 4 }$ 
D)  $x = 10 ; y = \frac { 5 } { 2 }$

Question 6

Solve the problem.
badges and vehicles. (Hint: Inscribe the star in a circle, and use the following theorem from
geometry: An angle whose vertex lies on the circumference of a circle is equal to half the central angle that
cuts off the same arc. See the figure.)

Accepted Answer

A)  $60 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $45 ^ { \circ }$ 
D)  $75 ^ { \circ }$ Answer: A
Explanation: 
A)  
B)  
C)  
D) 
10
The triangles are similar. Find the missing side, angle or value of the variable.
-Determine the measure of the angle in each point of the six-pointed star appearing on police badges and vehicles. (Hint: Inscribe the star in a circle, and use the following theorem from geometry: An angle whose vertex lies on the circumference of a circle is equal to half the central angle that
Cuts off the same arc. See the figure.)   
A)  $60 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $45 ^ { \circ }$ 
D)  $75 ^ { \circ }$ 
A)  $60 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $45 ^ { \circ }$ 
D)  $75 ^ { \circ }$ Answer: A
Explanation: 
A)  
B)  
C)  
D) 
10
The triangles are similar. Find the missing side, angle or value of the variable.
-Determine the measure of the angle in each point of the six-pointed star appearing on police badges and vehicles. (Hint: Inscribe the star in a circle, and use the following theorem from geometry: An angle whose vertex lies on the circumference of a circle is equal to half the central angle that
Cuts off the same arc. See the figure.)   
A)  $60 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $45 ^ { \circ }$ 
D)  $75 ^ { \circ }$

Question 7

Find the angle of least positive measure coterminal with the given angle.
-$\angle \mathrm { Q }$
 
$\begin{array}{l}
a=56^{\circ} \
b=6 \mathrm{~cm}
\end{array}$

Accepted Answer

A)  $34 ^ { \circ }$ 
B)  $56 ^ { \circ }$ 
C)  $6 \mathrm {~cm}$ 
D)  $90 ^ { \circ }$ 
A)  $34 ^ { \circ }$ 
B)  $56 ^ { \circ }$ 
C)  $6 \mathrm {~cm}$ 
D)  $90 ^ { \circ }$

Question 8

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
-sec ϴ = 0.97

Accepted Answer

A) Possible 
B) Impossible 
A) Possible 
B) Impossible

Question 9

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
-$$\mathrm { I } , \frac { \mathrm { r } } { \mathrm { y } }$$

Accepted Answer

A) Positive 
B) Negative 
A) Positive 
B) Negative

Question 10

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$\sin ^ { 2 } 360 ^ { \circ } + \cos ^ { 2 } 360 ^ { \circ }$

Accepted Answer

A)  1 
B)  2 
C)  $\sqrt { 3 }$ 
D)  $\sqrt { 2 }$ 
A)  1 
B)  2 
C)  $\sqrt { 3 }$ 
D)  $\sqrt { 2 }$

Question 11

Use the properties of angle measures to find the measure of each marked angle.
-

Accepted Answer

A)  Obtuse, scalene 
B)  Acute, equilateral 
C)  Obtuse, equilateral 
D)  Right, isosceles 
A)  Obtuse, scalene 
B)  Acute, equilateral 
C)  Obtuse, equilateral 
D)  Right, isosceles

Question 12

Use the fundamental identities to find the value of the trigonometric function.
-Find $\csc \theta$, given that $\cot \theta = - \sqrt { 15 }$ and $\theta$ is in quadrant II.

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $- \frac { 1 } { 4 }$ 
C)  $- 4$ 
D)  4 
A)  $\frac { 1 } { 4 }$ 
B)  $- \frac { 1 } { 4 }$ 
C)  $- 4$ 
D)  4

Question 13

Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
--47°

Accepted Answer

A) 43° 
B) 47° 
C) 313° 
D) 223° 
A) 43° 
B) 47° 
C) 313° 
D) 223°

Question 14

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
-$\csc \theta$, given that $\sin \theta = \frac { \sqrt { 11 } } { 6 }$

Accepted Answer

A)  $\frac { \sqrt { 11 } } { 11 }$ 
B)  $\frac { \sqrt { 11 } } { 6 }$ 
C)  $\frac { 11 \sqrt { 11 } } { 6 }$ 
D)  $\frac { 6 \sqrt { 11 } } { 11 }$ 
A)  $\frac { \sqrt { 11 } } { 11 }$ 
B)  $\frac { \sqrt { 11 } } { 6 }$ 
C)  $\frac { 11 \sqrt { 11 } } { 6 }$ 
D)  $\frac { 6 \sqrt { 11 } } { 11 }$

Question 15

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-

Accepted Answer

A)  $20 ^ { \circ }$ and $30 ^ { \circ }$ 
B)  $40 ^ { \circ }$ and $50 ^ { \circ }$ 
C)  $20 ^ { \circ }$ and $25 ^ { \circ }$ 
D)  $30 ^ { \circ }$ and $60 ^ { \circ }$ 
A)  $20 ^ { \circ }$ and $30 ^ { \circ }$ 
B)  $40 ^ { \circ }$ and $50 ^ { \circ }$ 
C)  $20 ^ { \circ }$ and $25 ^ { \circ }$ 
D)  $30 ^ { \circ }$ and $60 ^ { \circ }$

Question 16

Use the fundamental identities to find the value of the trigonometric function.
-Lines m and n are parallel.  
$a = ( 2 x + 9 ) ^ { \circ }$
$b = ( 3 x - 14 ) ^ { \circ }$

Accepted Answer

A)  $67 ^ { \circ } , 67 ^ { \circ }$ 
B)  $23 ^ { \circ } , 23 ^ { \circ }$ 
C)  $55 ^ { \circ } , 55 ^ { \circ }$ 
D)  $- 37 ^ { \circ } , - 37 ^ { \circ }$ 
A)  $67 ^ { \circ } , 67 ^ { \circ }$ 
B)  $23 ^ { \circ } , 23 ^ { \circ }$ 
C)  $55 ^ { \circ } , 55 ^ { \circ }$ 
D)  $- 37 ^ { \circ } , - 37 ^ { \circ }$

Question 17

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
-cot(n · 180°)

Accepted Answer

A) 0 
B) 1 
C) -1 
D) Undefined 
A) 0 
B) 1 
C) -1 
D) Undefined

Question 18

The triangles are similar. Find the missing side, angle or value of the variable.
-$\mathrm { II } , \frac { \mathrm { x } } { \mathrm { y } }$

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 19

The triangles are similar. Find the missing side, angle or value of the variable.
-50°

Accepted Answer

A) $230^{\circ} \text { and }-130^{\circ}$
 . 
B) $230^{\circ} \text { and }-130^{\circ}$
  
C) $410^{\circ} \text { and }-310^{\circ}$
  
D)  $410 ^ { \circ }$ and $- 310 ^ { \circ }$
  
A) $230^{\circ} \text { and }-130^{\circ}$
 . 
B) $230^{\circ} \text { and }-130^{\circ}$
  
C) $410^{\circ} \text { and }-310^{\circ}$
  
D)  $410 ^ { \circ }$ and $- 310 ^ { \circ }$

Question 20

If n is an integer, n · 180° represents an integer multiple of 180°, and (2n + 1) · 90° represents an odd integer multiple of
90°. Decide whether the expression is equal to 0, 1, -1, or is undefined.
-

Accepted Answer

A)  Acute, scalene 
B)  Obtuse, equilateral 
C)  Right, isosceles 
D)  Obtuse, isosceles 
A)  Acute, scalene 
B)  Obtuse, equilateral 
C)  Right, isosceles 
D)  Obtuse, isosceles

Solve the problem. - $\cot ^ { 2 } 90 ^ { \circ } - \sec 180 ^ { \circ }$

Use the fundamental identities to find the value of the trigonometric function. -Find the complement of an angle whose measure is 33°21´.

Evaluate the expression. -AC

Find the measure of each angle in the problem. -Complementary angles with measures 3x and 6x - 18 degrees

Find the angle of least positive measure coterminal with the given angle. -x and y

Find the angle of least positive measure coterminal with the given angle. - $\angle \mathrm { Q }$ $Find the angle of least positive measure coterminal with the given angle. - \angle \mathrm { Q } \begin{array}{l} a=56^{\circ} \\ b=6 \mathrm{~cm} \end{array}$ a=5 b=6

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. -sec ϴ = 0.97

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - $\mathrm { I } , \frac { \mathrm { r } } { \mathrm { y } }$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $\sin ^ { 2 } 360 ^ { \circ } + \cos ^ { 2 } 360 ^ { \circ }$

Use the properties of angle measures to find the measure of each marked angle. -

Use the fundamental identities to find the value of the trigonometric function. -Find $\csc \theta$ , given that $\cot \theta = - \sqrt { 15 }$ and $\theta$ is in quadrant II.

Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the indicated trig function for . --47°

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - $\csc \theta$ , given that $\sin \theta = \frac { \sqrt { 11 } } { 6 }$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -cot(n · 180°)

The triangles are similar. Find the missing side, angle or value of the variable. - $\mathrm { II } , \frac { \mathrm { x } } { \mathrm { y } }$

The triangles are similar. Find the missing side, angle or value of the variable. -50°

If n is an integer, n · 180° represents an integer multiple of 180°, and (2n + 1) · 90° represents an odd integer multiple of 90°. Decide whether the expression is equal to 0, 1, -1, or is undefined. -

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Exam 1: Trigonometric Functions

Solve the problem. - cot⁡290∘−sec⁡180∘\cot ^ { 2 } 90 ^ { \circ } - \sec 180 ^ { \circ }cot290∘−sec180∘