Question 1

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement.
-cot ϴ= 4.167

Accepted Answer

A) -13.49° 
B) 13.49° 
C) 13.89° 
D) 76.11° 
A) -13.49° 
B) 13.49° 
C) 13.89° 
D) 76.11°

Question 2

Find the exact function value if it exists.
-cot (-90°)

Accepted Answer

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

Question 3

From the top of a vertical tower, 310 feet above the the surface of the earth, the angle of depression to a doghouse is 24° 34'. How far is it from the doghouse to the foot of the tower? Round your
Answer to the nearest hundredth.

Accepted Answer

A) 678.14ft 
B) 780.74 ft 
C) 662.55 ft 
D) 690.54 ft 
A) 678.14ft 
B) 780.74 ft 
C) 662.55 ft 
D) 690.54 ft

Question 4

Use a calculator to find the function value to four decimal places.
-sec 10°5'

Accepted Answer

A) 2.0314 
B) 1.0147 
C) 1.0157 
D) 2.0324 
A) 2.0314 
B) 1.0147 
C) 1.0157 
D) 2.0324

Question 5

$\cos \left( - 300 ^ { \circ } \right)$

Accepted Answer

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

Question 6

Solve the right triangle.
-a = 11.6, c = 22.6, C = 90°

Accepted Answer

A) A = 62.8°, B = 27.2°, b = 25.4 
B) A = 30.9°, B = 30.9°, b = 19.4 
C) A = 30.9°, B = 59.1°, b = 25.4 
D) A = 30.9°, B = 59.1°, b = 19.4 
A) A = 62.8°, B = 27.2°, b = 25.4 
B) A = 30.9°, B = 30.9°, b = 19.4 
C) A = 30.9°, B = 59.1°, b = 25.4 
D) A = 30.9°, B = 59.1°, b = 19.4

Question 7

Find the signs of the six trigonometric functions for the given angle.
--110°

Accepted Answer

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

Question 8

Suppose ABC is a right triangle with sides of length a, b, and c and right angle at C. Find the exact value of the indicated
trigonometric function. You may need to use the Pythagorean theorem to find the unknown side length. Rationalize the
denominator if necessary.
-Find $\tan \mathrm { A }$ when $\mathrm { a } = 2$ and $\mathrm { b } = 3$.

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B)  $\frac { \sqrt { 13 } } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { \sqrt { 13 } } { 2 }$ 
A)  $\frac { 3 } { 2 }$ 
B)  $\frac { \sqrt { 13 } } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { \sqrt { 13 } } { 2 }$

Question 9

$\tan \left( - 315 ^ { \circ } \right)$

Accepted Answer

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

Question 10

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative.
-II, $\frac { x } { y }$

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

What is the angle of elevation of the sun when a 35-ft flag pole casts a 24-ft shadow? Round to the nearest tenth of a degree.

Accepted Answer

A) 43.3° 
B) 34.4° 
C) 55.6° 
D) 46.7° 
A) 43.3° 
B) 34.4° 
C) 55.6° 
D) 46.7°

Question 14

A 39-foot ladder is leaning against the side of a building. If the ladder makes an angle of 24° 42' with the side of the building, how far is the bottom of the ladder from the base of the building?
Round your answer to the hundredths place.

Accepted Answer

A) 22 ft 
B) 6.93 ft 
C) 17.6 ft 
D) 16.3 ft 
A) 22 ft 
B) 6.93 ft 
C) 17.6 ft 
D) 16.3 ft

Question 15

Find the angle of smallest possible positive measure coterminal with the given angle.
-859°

Accepted Answer

A) 489° 
B) 129° 
C) 499° 
D) 139° 
A) 489° 
B) 129° 
C) 499° 
D) 139°

Question 16

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.
-65°

Accepted Answer

A)  $245 ^ { \circ }$ and $- 115 ^ { \circ }$
  
B)  $245 ^ { \circ }$ and $- 115 ^ { \circ }$
  
C)  $425^{\circ} \text { and }-295^{\circ}$
  
D)  $425 ^ { \circ }$ and $- 295 ^ { \circ }$
  
A)  $245 ^ { \circ }$ and $- 115 ^ { \circ }$
  
B)  $245 ^ { \circ }$ and $- 115 ^ { \circ }$
  
C)  $425^{\circ} \text { and }-295^{\circ}$
  
D)  $425 ^ { \circ }$ and $- 295 ^ { \circ }$

Question 17

Suppose ABC is a right triangle with sides of length a, b, and c and right angle at C. Find the exact value of the indicated
trigonometric function. You may need to use the Pythagorean theorem to find the unknown side length. Rationalize the
denominator if necessary.
-Find $\cos \mathrm { A }$ when $a = 2$ and $b = 7$.

Accepted Answer

A)  $\frac { 7 \sqrt { 53 } } { 53 }$ 
B)  $\frac { \sqrt { 53 } } { 2 }$ 
C)  $\frac { 2 \sqrt { 53 } } { 53 }$ 
D)  $\frac { \sqrt { 53 } } { 7 }$ 
A)  $\frac { 7 \sqrt { 53 } } { 53 }$ 
B)  $\frac { \sqrt { 53 } } { 2 }$ 
C)  $\frac { 2 \sqrt { 53 } } { 53 }$ 
D)  $\frac { \sqrt { 53 } } { 7 }$

Question 18

State in which quadrant the terminal side of the given angle lies.
--337°

Accepted Answer

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

Question 19

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-97°17'13''

Accepted Answer

A) 97.30 
B) 97.29 
C) 97.25 
D) 97.35 
A) 97.30 
B) 97.29 
C) 97.25 
D) 97.35

Question 20

Find the exact value of the function. Rationalize the denominator if necessary.
-sec 240°

Accepted Answer

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

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -cot ϴ= 4.167

Find the exact function value if it exists. -cot (-90°)

From the top of a vertical tower, 310 feet above the the surface of the earth, the angle of depression to a doghouse is 24° 34'. How far is it from the doghouse to the foot of the tower? Round your Answer to the nearest hundredth.

Use a calculator to find the function value to four decimal places. -sec 10°5'

$\cos \left( - 300 ^ { \circ } \right)$

Solve the right triangle. -a = 11.6, c = 22.6, C = 90°

Find the signs of the six trigonometric functions for the given angle. --110°

$\tan \left( - 315 ^ { \circ } \right)$

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -II, $\frac { x } { y }$

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

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

What is the angle of elevation of the sun when a 35-ft flag pole casts a 24-ft shadow? Round to the nearest tenth of a degree.

A 39-foot ladder is leaning against the side of a building. If the ladder makes an angle of 24° 42' with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place.

Find the angle of smallest possible positive measure coterminal with the given angle. -859°

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. -65°

State in which quadrant the terminal side of the given angle lies. --337°

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -97°17'13''

Find the exact value of the function. Rationalize the denominator if necessary. -sec 240°

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Exam 14: Trigonometry Formerly

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -cot ϴ= 4.167

Find the exact function value if it exists. -cot (-90°)

From the top of a vertical tower, 310 feet above the the surface of the earth, the angle of depression to a doghouse is 24° 34'. How far is it from the doghouse to the foot of the tower? Round your Answer to the nearest hundredth.

Use a calculator to find the function value to four decimal places. -sec 10°5'

cos⁡(−300∘)\cos \left( - 300 ^ { \circ } \right)cos(−300∘)

Solve the right triangle. -a = 11.6, c = 22.6, C = 90°

Find the signs of the six trigonometric functions for the given angle. --110°

tan⁡(−315∘)\tan \left( - 315 ^ { \circ } \right)tan(−315∘)

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -II, xy\frac { x } { y }yx​

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

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

What is the angle of elevation of the sun when a 35-ft flag pole casts a 24-ft shadow? Round to the nearest tenth of a degree.

A 39-foot ladder is leaning against the side of a building. If the ladder makes an angle of 24° 42' with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place.

Find the angle of smallest possible positive measure coterminal with the given angle. -859°

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. -65°

State in which quadrant the terminal side of the given angle lies. --337°

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -97°17'13''

Find the exact value of the function. Rationalize the denominator if necessary. -sec 240°

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

$\cos \left( - 300 ^ { \circ } \right)$

$\tan \left( - 315 ^ { \circ } \right)$

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -II, $\frac { x } { y }$

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