Question 1

Provide an appropriate response.
-Find $\cot \theta$, given that $\tan \theta = \frac { \sqrt { 7 } } { 3 }$ and $\theta$ is in quadrant III.

Accepted Answer

A)  $\frac { 3 \sqrt { 7 } } { 7 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $- \frac { \sqrt { 7 } } { 9 }$ 
A)  $\frac { 3 \sqrt { 7 } } { 7 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $- \frac { \sqrt { 7 } } { 9 }$

Question 2

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.
-153.38°

Accepted Answer

A) 153°22´38´´ 
B) 153°20´38´´ 
C) 153°22´48´´ 
D) 153°23´48´´ 
A) 153°22´38´´ 
B) 153°20´38´´ 
C) 153°22´48´´ 
D) 153°23´48´´

Question 3

Identify the quadrant for the angle satisfying the following conditions.
-cot ϴ > 0 and sin ϴ < 0

Accepted Answer

A) Quadrant I 
B) Quadrant IV 
C) Quadrant III 
D) Quadrant II 
A) Quadrant I 
B) Quadrant IV 
C) Quadrant III 
D) Quadrant II

Question 4

Find the measure of each angle in the problem.
-

Accepted Answer

A)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
B)  $90 ^ { \circ }$ and $270 ^ { \circ }$ 
C)  $45 ^ { \circ }$ and $55 ^ { \circ }$ 
D)  $45 ^ { \circ }$ and $135 ^ { \circ }$ 
A)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
B)  $90 ^ { \circ }$ and $270 ^ { \circ }$ 
C)  $45 ^ { \circ }$ and $55 ^ { \circ }$ 
D)  $45 ^ { \circ }$ and $135 ^ { \circ }$

Question 5

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.
-$\tan \theta$, given that $\cot \theta = - \frac { 10 } { 11 }$

Accepted Answer

A)  $\frac { 21 } { 11 }$ 
B)  $\frac { 11 } { 10 }$ 
C)  $- \frac { 10 } { 11 }$ 
D)  $- \frac { 11 } { 10 }$ 
A)  $\frac { 21 } { 11 }$ 
B)  $\frac { 11 } { 10 }$ 
C)  $- \frac { 10 } { 11 }$ 
D)  $- \frac { 11 } { 10 }$

Question 6

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-Find $\sec \theta$, given that $\tan \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant $\mathrm { I }$.

Accepted Answer

A)  $\frac { 5 } { 4 }$ 
B)  $- \frac { \sqrt { 7 } } { 9 }$ 
C)  $\frac { 3 \sqrt { 7 } } { 7 }$ 
D)  $- \frac { 3 } { 2 }$ 
A)  $\frac { 5 } { 4 }$ 
B)  $- \frac { \sqrt { 7 } } { 9 }$ 
C)  $\frac { 3 \sqrt { 7 } } { 7 }$ 
D)  $- \frac { 3 } { 2 }$

Question 7

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
-$$\sin \theta = 0.6 \text { and } \csc \theta = - 0.6$$

Accepted Answer

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

Question 8

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
-(0, -5)

Accepted Answer

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

Question 9

Evaluate the expression.
-40° and 80°

Accepted Answer

A) -30° 
B) 60° 
C) 120° 
D) 240° 
A) -30° 
B) 60° 
C) 120° 
D) 240°

Question 10

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or
negative.
-115°

Accepted Answer

A) $475^{\circ} \text { and }-245^{\circ}$
  
B) $295^{\circ} \text { and }-65^{\circ}$
  
C)  $475 ^ { \circ }$ and $- 245 ^ { \circ }$
  
D)  $295 ^ { \circ }$ and $- 65 ^ { \circ }$
  
A) $475^{\circ} \text { and }-245^{\circ}$
  
B) $295^{\circ} \text { and }-65^{\circ}$
  
C)  $475 ^ { \circ }$ and $- 245 ^ { \circ }$
  
D)  $295 ^ { \circ }$ and $- 65 ^ { \circ }$

Question 11

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

$a = 14$
$b = 21$
$c = 10$
$d = 15$
$e = 20$

Accepted Answer

A)  $x = 28$ 
B)  $x = 26$ 
C)  $x = 20$ 
D)  $x = 35$ 
A)  $x = 28$ 
B)  $x = 26$ 
C)  $x = 20$ 
D)  $x = 35$

Question 12

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.
-

Accepted Answer

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

Question 13

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or
negative.
-III, $\frac { r } { x }$

Accepted Answer

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

Question 14

Find the measure of each angle in the problem.
-cos ϴ, given that sec ϴ = -7

Accepted Answer

A)  $\frac { 1 } { 7 }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $- \frac { 1 } { 7 }$ 
A)  $\frac { 1 } { 7 }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $- \frac { 1 } { 7 }$

Question 15

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

Accepted Answer

A)  $70 ^ { \circ }$ and $20 ^ { \circ }$ 
B)  $35 ^ { \circ }$ and $10 ^ { \circ }$ 
C)  $140 ^ { \circ }$ and $40 ^ { \circ }$ 
D)  $65 ^ { \circ }$ and $35 ^ { \circ }$ 
A)  $70 ^ { \circ }$ and $20 ^ { \circ }$ 
B)  $35 ^ { \circ }$ and $10 ^ { \circ }$ 
C)  $140 ^ { \circ }$ and $40 ^ { \circ }$ 
D)  $65 ^ { \circ }$ and $35 ^ { \circ }$

Question 16

Evaluate the expression.
-202.61°

Accepted Answer

A) 202°37´35´´ 
B) 202°36´61´´ 
C) 202°35´61´´ 
D) 202°36´36´´ 
A) 202°37´35´´ 
B) 202°36´61´´ 
C) 202°35´61´´ 
D) 202°36´36´´

Question 17

Provide an appropriate response.
-For what angle $\mathrm { T }$ is $\sin \mathrm { T } \approx 0.574$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$.)

Accepted Answer

A)  $46.917 ^ { \circ }$ 
B)  $0.574 ^ { \circ }$ 
C)  $55 ^ { \circ }$ 
D)  $35 ^ { \circ }$ 
A)  $46.917 ^ { \circ }$ 
B)  $0.574 ^ { \circ }$ 
C)  $55 ^ { \circ }$ 
D)  $35 ^ { \circ }$

Question 18

Solve the problem.
-Find the measure of the smaller angle formed by the hands of the clock shown.

Accepted Answer

A)  $150 ^ { \circ }$ 
B)  $110 ^ { \circ }$ 
C)  $120 ^ { \circ }$ 
D)  $60 ^ { \circ }$ 
A)  $150 ^ { \circ }$ 
B)  $110 ^ { \circ }$ 
C)  $120 ^ { \circ }$ 
D)  $60 ^ { \circ }$

Question 19

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.
-951°

Accepted Answer

A) 221° 
B) 581° 
C) 231° 
D) 591° 
A) 221° 
B) 581° 
C) 231° 
D) 591°

Question 20

Use the properties of angle measures to find the measure of each marked angle.
-180° - 8°45´27´´

Accepted Answer

A) 171°15´33´´ 
B) 172°14´33´´ 
C) 172°15´33´´ 
D) 171°14´33´´ 
A) 171°15´33´´ 
B) 172°14´33´´ 
C) 172°15´33´´ 
D) 171°14´33´´

Provide an appropriate response. -Find $\cot \theta$ , given that $\tan \theta = \frac { \sqrt { 7 } } { 3 }$ and $\theta$ is in quadrant III.

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. -153.38°

Identify the quadrant for the angle satisfying the following conditions. -cot ϴ > 0 and sin ϴ < 0

Find the measure of each angle in the problem. -

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. - $\tan \theta$ , given that $\cot \theta = - \frac { 10 } { 11 }$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -Find $\sec \theta$ , given that $\tan \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant $\mathrm { I }$ .

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. - $\sin \theta = 0.6 \text { and } \csc \theta = - 0.6$

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. -(0, -5)

Evaluate the expression. -40° and 80°

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. -115°

The triangles are similar. Find the missing side, angle or value of the variable. - $a = 14$ $b = 21$ $c = 10$ $d = 15$ $e = 20$

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. -

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. -III, $\frac { r } { x }$

Find the measure of each angle in the problem. -cos ϴ, given that sec ϴ = -7

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

Evaluate the expression. -202.61°

Provide an appropriate response. -For what angle $\mathrm { T }$ is $\sin \mathrm { T } \approx 0.574$ ? (Assume $0 ^ { \circ } \leq \mathrm { T } \leq 90 ^ { \circ }$ .)

Solve the problem. -Find the measure of the smaller angle formed by the hands of the clock shown.

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. -951°

Use the properties of angle measures to find the measure of each marked angle. -180° - 8°45´27´´

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

Provide an appropriate response. -Find cot⁡θ\cot \thetacotθ , given that tan⁡θ=73\tan \theta = \frac { \sqrt { 7 } } { 3 }tanθ=37​​ and θ\thetaθ is in quadrant III.