Question 1

Find the signs of the six trigonometric functions for the given angle.
-551°

Accepted Answer

A) Negative: all 
B) Positive: cosine and secant; negative: sine, tangent, cotangent, cosecant 
C) Positive: sine and cosecant; negative: cosine, tangent, cotangent, secant 
D) Positive: tangent and cotangent; negative: sine, cosine, secant, cosecant 
A) Negative: all 
B) Positive: cosine and secant; negative: sine, tangent, cotangent, cosecant 
C) Positive: sine and cosecant; negative: cosine, tangent, cotangent, secant 
D) Positive: tangent and cotangent; negative: sine, cosine, secant, cosecant

Question 2

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement.
-csc ϴ= 2.877

Accepted Answer

A) 19.17° 
B) -19.17° 
C) 69.66° 
D) 20.34° 
A) 19.17° 
B) -19.17° 
C) 69.66° 
D) 20.34°

Question 3

$$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$$
-$\sin \theta = - \frac { 1 } { 2 }$

Accepted Answer

A)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
B)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
C)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
D)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
A)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
B)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
C)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
D)  $60 ^ { \circ }$ and $120 ^ { \circ }$

Question 4

State in which quadrant the terminal side of the given angle lies.
-856°

Accepted Answer

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

Question 5

$$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$$
-$\cos \theta = - \frac { \sqrt { 3 } } { 2 }$

Accepted Answer

A)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
B)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
C)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
D)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
A)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
B)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
C)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
D)  $60 ^ { \circ }$ and $120 ^ { \circ }$

Question 6

Find the signs of the six trigonometric functions for the given angle.
--358°

Accepted Answer

A) Positive: cosine and secant; negative: sine, tangent, cotangent, secant 
B) Positive: sine, cosine; negative: tangent, cotangent, secant, cosecant 
C) Positive: tangent and cotangent; negative: sine, cosine, secant, cosecant 
D) Positive: all 
A) Positive: cosine and secant; negative: sine, tangent, cotangent, secant 
B) Positive: sine, cosine; negative: tangent, cotangent, secant, cosecant 
C) Positive: tangent and cotangent; negative: sine, cosine, secant, cosecant 
D) Positive: all

Question 7

$$\cos \left( - 690 ^ { \circ } \right)$$

Accepted Answer

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

Question 8

State in which quadrant the terminal side of the given angle lies.
-1293°

Accepted Answer

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

Question 9

At an altitude of 2600 ft, the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 3 miles away (to the nearest tenth of a degree)? Note that 1 mile = 5280 feet.

Accepted Answer

A) 88.9° 
B) 9.3° 
C) 89.9° 
D) 10.3° 
A) 88.9° 
B) 9.3° 
C) 89.9° 
D) 10.3°

Question 10

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary.
-$\csc \theta$, if $\sin \theta = \frac { \sqrt { 11 } } { 6 }$

Accepted Answer

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

Question 11

The angle of elevation from a point on the ground to the top of a tower is 36° 12'. The angle of elevation from a point 164 feet farther back from the tower is 21° 15'. Find the height
Of the tower. Round your answer to the hundredths place.

Accepted Answer

A) 146.58 ft 
B) 1360.8 ft 
C) 131.84 ft 
D) 136.08 ft 
A) 146.58 ft 
B) 1360.8 ft 
C) 131.84 ft 
D) 136.08 ft

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.
-295°

Accepted Answer

A)  $65 ^ { \circ }$ and $- 65 ^ { \circ }$
  
B)  $85 ^ { \circ }$ and $- 95 ^ { \circ }$
  
C)  $655 ^ { \circ }$ and $- 65 ^ { \circ }$
  
D)  $755 ^ { \circ }$ and $- 105 ^ { \circ }$
  
A)  $65 ^ { \circ }$ and $- 65 ^ { \circ }$
  
B)  $85 ^ { \circ }$ and $- 95 ^ { \circ }$
  
C)  $655 ^ { \circ }$ and $- 65 ^ { \circ }$
  
D)  $755 ^ { \circ }$ and $- 105 ^ { \circ }$

Question 13

$\sin \left( - 135 ^ { \circ } \right)$

Accepted Answer

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

Question 14

$\cos \left( - 240 ^ { \circ } \right)$

Accepted Answer

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

Question 15

Use the fundamental identities to find the value of the trigonometric function.
-$\sin \alpha$, if $\cot \alpha = 3$ and $\cos \alpha < 0$

Accepted Answer

A)  $- \frac { 3 \sqrt { 10 } } { 10 }$ 
B)  $\frac { \sqrt { 10 } } { 10 }$ 
C)  $- \sqrt { 10 }$ 
D)  $- \frac { \sqrt { 10 } } { 10 }$ 
A)  $- \frac { 3 \sqrt { 10 } } { 10 }$ 
B)  $\frac { \sqrt { 10 } } { 10 }$ 
C)  $- \sqrt { 10 }$ 
D)  $- \frac { \sqrt { 10 } } { 10 }$

Question 16

State in which quadrant the terminal side of the given angle lies.
-322°25'35''

Accepted Answer

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

Question 17

Find the exact function value if it exists.
-tan 180°

Accepted Answer

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

Question 18

Find the signs of the six trigonometric functions for the given angle.
--210°

Accepted Answer

A) Positive: tangent and cotangent; negative: sine, cosine, secant, cosecant 
B) Positive: sine and cosecant; negative: cosine, tangent, cotangent, secant 
C) Positive: cosine and secant; negative: sine, tangent, cotangent, cosecant 
D) Negative: all 
A) Positive: tangent and cotangent; negative: sine, cosine, secant, cosecant 
B) Positive: sine and cosecant; negative: cosine, tangent, cotangent, secant 
C) Positive: cosine and secant; negative: sine, tangent, cotangent, cosecant 
D) Negative: all

Question 19

Convert the angle to degrees, minutes, and seconds.
-108.26°

Accepted Answer

A) 108°15'40'' 
B) 108°28'26'' 
C) 108°15'36'' 
D) 108°15'28'' 
A) 108°15'40'' 
B) 108°28'26'' 
C) 108°15'36'' 
D) 108°15'28''

Question 20

Perform the calculation.
-92°27' - 28°38'

Accepted Answer

A) 63°49' 
B) 120°65' 
C) 64°11' 
D) 64°38' 
A) 63°49' 
B) 120°65' 
C) 64°11' 
D) 64°38'

Find the signs of the six trigonometric functions for the given angle. -551°

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -csc ϴ= 2.877

$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$ - $\sin \theta = - \frac { 1 } { 2 }$

State in which quadrant the terminal side of the given angle lies. -856°

$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$ - $\cos \theta = - \frac { \sqrt { 3 } } { 2 }$

Find the signs of the six trigonometric functions for the given angle. --358°

$\cos \left( - 690 ^ { \circ } \right)$

State in which quadrant the terminal side of the given angle lies. -1293°

At an altitude of 2600 ft, the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 3 miles away (to the nearest tenth of a degree)? Note that 1 mile = 5280 feet.

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\csc \theta$ , if $\sin \theta = \frac { \sqrt { 11 } } { 6 }$

The angle of elevation from a point on the ground to the top of a tower is 36° 12'. The angle of elevation from a point 164 feet farther back from the tower is 21° 15'. Find the height Of the tower. Round your answer to the hundredths place.

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. -295°

$\sin \left( - 135 ^ { \circ } \right)$

$\cos \left( - 240 ^ { \circ } \right)$

Use the fundamental identities to find the value of the trigonometric function. - $\sin \alpha$ , if $\cot \alpha = 3$ and $\cos \alpha < 0$

State in which quadrant the terminal side of the given angle lies. -322°25'35''

Find the exact function value if it exists. -tan 180°

Find the signs of the six trigonometric functions for the given angle. --210°

Convert the angle to degrees, minutes, and seconds. -108.26°

Perform the calculation. -92°27' - 28°38'

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Graph Theory

Voting and Apportionment

Filters

Exam 14: Trigonometry Formerly

Find the signs of the six trigonometric functions for the given angle. -551°

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -csc ϴ= 2.877

State in which quadrant the terminal side of the given angle lies. -856°

Find the signs of the six trigonometric functions for the given angle. --358°

cos⁡(−690∘)\cos \left( - 690 ^ { \circ } \right)cos(−690∘)

State in which quadrant the terminal side of the given angle lies. -1293°

At an altitude of 2600 ft, the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 3 miles away (to the nearest tenth of a degree)? Note that 1 mile = 5280 feet.

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - csc⁡θ\csc \thetacscθ , if sin⁡θ=116\sin \theta = \frac { \sqrt { 11 } } { 6 }sinθ=611​​

The angle of elevation from a point on the ground to the top of a tower is 36° 12'. The angle of elevation from a point 164 feet farther back from the tower is 21° 15'. Find the height Of the tower. Round your answer to the hundredths place.

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. -295°

sin⁡(−135∘)\sin \left( - 135 ^ { \circ } \right)sin(−135∘)

cos⁡(−240∘)\cos \left( - 240 ^ { \circ } \right)cos(−240∘)

Use the fundamental identities to find the value of the trigonometric function. - sin⁡α\sin \alphasinα , if cot⁡α=3\cot \alpha = 3cotα=3 and cos⁡α<0\cos \alpha < 0cosα<0

State in which quadrant the terminal side of the given angle lies. -322°25'35''

Find the exact function value if it exists. -tan 180°

Find the signs of the six trigonometric functions for the given angle. --210°

Convert the angle to degrees, minutes, and seconds. -108.26°

Perform the calculation. -92°27' - 28°38'

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Graph Theory

Voting and Apportionment

Filters

$\cos \left( - 690 ^ { \circ } \right)$

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\csc \theta$ , if $\sin \theta = \frac { \sqrt { 11 } } { 6 }$

$\sin \left( - 135 ^ { \circ } \right)$

$\cos \left( - 240 ^ { \circ } \right)$

Use the fundamental identities to find the value of the trigonometric function. - $\sin \alpha$ , if $\cot \alpha = 3$ and $\cos \alpha < 0$