Question 1

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary.
-$\cos \theta$, if $\sec \theta = - 9.5$

Accepted Answer

A)  $\frac { 2 } { 19 }$ 
B)  $- \frac { 19 } { 2 }$ 
C)  $\frac { 17 } { 19 }$ 
D)  $- \frac { 2 } { 19 }$ 
A)  $\frac { 2 } { 19 }$ 
B)  $- \frac { 19 } { 2 }$ 
C)  $\frac { 17 } { 19 }$ 
D)  $- \frac { 2 } { 19 }$

Question 2

State in which quadrant the terminal side of the given angle lies.
-218°28'

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Solve the problem.
-From a boat on the river below a dam, the angle of elevation to the top of the dam is 34°48'. If the top of the dam is 2064 feet above the level of the river, how far is the boat from the base of the dam
(to the nearest foot)?

Accepted Answer

A) 2940 ft 
B) 2950 ft 
C) 2970 ft 
D) 2960 ft 
A) 2940 ft 
B) 2950 ft 
C) 2970 ft 
D) 2960 ft

Question 5

cot (-240°)

Accepted Answer

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

Question 6

Write the expression in terms of its cofunction.
-tan 42°

Accepted Answer

A) cot 132° 
B) sec 42° 
C) cot 48° 
D) cot 42° 
A) cot 132° 
B) sec 42° 
C) cot 48° 
D) cot 42°

Question 7

Solve for the requested quantity.
-Find b. Round your answer to the hundredths place.

Accepted Answer

A)  $b = 3035.68 \mathrm {~m} \quad \mathrm {~b}$ 
B)  $b = 3014.11 \mathrm {~m}$ 
C)  $b = 3029.41 \mathrm {~m}$ 
D)  $b = 2984.02 \mathrm {~m}$ 
A)  $b = 3035.68 \mathrm {~m} \quad \mathrm {~b}$ 
B)  $b = 3014.11 \mathrm {~m}$ 
C)  $b = 3029.41 \mathrm {~m}$ 
D)  $b = 2984.02 \mathrm {~m}$

Question 8

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions.
-$\sec \theta < 0$

Accepted Answer

A)  Quadrants III or IV 
B)  Quadrants II or IV 
C)  Quadrant III 
D)  Quadrants II or III 
A)  Quadrants III or IV 
B)  Quadrants II or IV 
C)  Quadrant III 
D)  Quadrants II or III

Question 9

Perform the calculation.
-180° - 23°31'27''

Accepted Answer

A) 157°29'33'' 
B) 157°28'33'' 
C) 156°29'33'' 
D) 156°28'33'' 
A) 157°29'33'' 
B) 157°28'33'' 
C) 156°29'33'' 
D) 156°28'33''

Question 10

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$. Give the exact value of the indicated trig function for $\theta$. Rationalize the denominator if necessary. If the function is undefined, say so.
-$( - 8 , - 5 )$; find $\cot \theta$

Accepted Answer

A)  $- \frac { 5 } { 9 }$ 
B)  $\frac { 8 } { 5 }$ 
C)  $- \frac { 8 } { 9 }$ 
D)  $\frac { 5 } { 8 }$ 
A)  $- \frac { 5 } { 9 }$ 
B)  $\frac { 8 } { 5 }$ 
C)  $- \frac { 8 } { 9 }$ 
D)  $\frac { 5 } { 8 }$

Question 11

Solve the right triangle.
-B = 36.9°, c = 2.5 mm, C = 90°

Accepted Answer

A) a = 1.2 mm, A = 53.1°, b = 2.2 cm 
B) a = 1.5 mm, A = 53.1°, b = 2.0 mm 
C) a = 2.0 mm, A = 53.1°, b = 1.2 mm 
D) a = 2.0 mm, A = 53.1°, b = 1.5 mm 
A) a = 1.2 mm, A = 53.1°, b = 2.2 cm 
B) a = 1.5 mm, A = 53.1°, b = 2.0 mm 
C) a = 2.0 mm, A = 53.1°, b = 1.2 mm 
D) a = 2.0 mm, A = 53.1°, b = 1.5 mm

Question 12

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

Accepted Answer

A)  $45 ^ { \circ }$ and $225 ^ { \circ }$ 
B)  $135 ^ { \circ }$ and $225 ^ { \circ }$ 
C)  $45 ^ { \circ }$ and $315 ^ { \circ }$ 
D)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
A)  $45 ^ { \circ }$ and $225 ^ { \circ }$ 
B)  $135 ^ { \circ }$ and $225 ^ { \circ }$ 
C)  $45 ^ { \circ }$ and $315 ^ { \circ }$ 
D)  $225 ^ { \circ }$ and $315 ^ { \circ }$

Question 13

State in which quadrant the terminal side of the given angle lies.
--195.4°

Accepted Answer

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

Question 14

Solve the right triangle.
-A = 50° 28', c = 249 m , C = 90°

Accepted Answer

A) B = 40° 28', a = 192.24 m, b = 158.5 m 
B) B = 39° 32', a = 192.04 m, b = 158.5 m 
C) B = 39° 32', a = 192.24 m, b = 165.5 m 
D) B = 39° 28', a = 193.24 m, b = 151.5 m 
A) B = 40° 28', a = 192.24 m, b = 158.5 m 
B) B = 39° 32', a = 192.04 m, b = 158.5 m 
C) B = 39° 32', a = 192.24 m, b = 165.5 m 
D) B = 39° 28', a = 193.24 m, b = 151.5 m

Question 15

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
- 
Find $\cos B$ and $\cot B$.

Accepted Answer

A)  $\cos B = \frac { 40 } { 41 } ; \cot B = \frac { 40 } { 9 }$ 
B)  $\cos \mathrm { B } = \frac { 41 } { 40 } ; \cot \mathrm { B } = \frac { 9 } { 40 }$ 
C)  $\cos \mathrm { B } = \frac { 9 } { 40 } ; \cot \mathrm { B } = \frac { 40 } { 9 }$ 
D)  $\cos B = \frac { 9 } { 41 } ; \cot B = \frac { 9 } { 40 }$ 
A)  $\cos B = \frac { 40 } { 41 } ; \cot B = \frac { 40 } { 9 }$ 
B)  $\cos \mathrm { B } = \frac { 41 } { 40 } ; \cot \mathrm { B } = \frac { 9 } { 40 }$ 
C)  $\cos \mathrm { B } = \frac { 9 } { 40 } ; \cot \mathrm { B } = \frac { 40 } { 9 }$ 
D)  $\cos B = \frac { 9 } { 41 } ; \cot B = \frac { 9 } { 40 }$

Question 16

Find the reference angle for the given angle.
-A = -14.3°

Accepted Answer

A) 76.2° 
B) 75.7° 
C) 14.3° 
D) 14.8° 
A) 76.2° 
B) 75.7° 
C) 14.3° 
D) 14.8°

Question 17

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

Accepted Answer

A)  $45 ^ { \circ }$ and $225 ^ { \circ }$ 
B)  $45 ^ { \circ }$ and $315 ^ { \circ }$ 
C)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
D)  $135 ^ { \circ }$ and $225 ^ { \circ }$ 
A)  $45 ^ { \circ }$ and $225 ^ { \circ }$ 
B)  $45 ^ { \circ }$ and $315 ^ { \circ }$ 
C)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
D)  $135 ^ { \circ }$ and $225 ^ { \circ }$

Question 18

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$. Give the exact value of the indicated trig function for $\theta$. Rationalize the denominator if necessary. If the function is undefined, say so.
-$( - 5 , \sqrt { 3 } )$; find $\sec \theta$

Accepted Answer

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

Question 19

Solve for the requested quantity.
-Find all missing sides and angles. Round to the nearest tenth.  
b = 25
$B = 35 ^ { \circ } 35 ^ { \prime }$

Accepted Answer

A)  $\mathrm { A } = 54 ^ { \circ } 25 ^ { \prime } , \mathrm { c } = 43 , \mathrm { a } = 30.7$ 
B)  $\mathrm { A } = 54 ^ { \circ } 25 ^ { \prime } , \mathrm { c } = 43 , \mathrm { a } = 34.9$ 
C)  $\mathrm { A } = 54 ^ { \circ } 25 ^ { \prime } , \mathrm { c } = 43.2 , \mathrm { a } = 30.7$ 
D)  $A = 54 ^ { \circ } 25 ^ { \prime } , \mathrm { c } = 30.7 , \mathrm { a } = 43$ 
A)  $\mathrm { A } = 54 ^ { \circ } 25 ^ { \prime } , \mathrm { c } = 43 , \mathrm { a } = 30.7$ 
B)  $\mathrm { A } = 54 ^ { \circ } 25 ^ { \prime } , \mathrm { c } = 43 , \mathrm { a } = 34.9$ 
C)  $\mathrm { A } = 54 ^ { \circ } 25 ^ { \prime } , \mathrm { c } = 43.2 , \mathrm { a } = 30.7$ 
D)  $A = 54 ^ { \circ } 25 ^ { \prime } , \mathrm { c } = 30.7 , \mathrm { a } = 43$

Question 20

Convert the angle to degrees, minutes, and seconds.
-246.06°

Accepted Answer

A) 246°3'36'' 
B) 246°35'6'' 
C) 246°3'6'' 
D) 246°4'35'' 
A) 246°3'36'' 
B) 246°35'6'' 
C) 246°3'6'' 
D) 246°4'35''

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\cos \theta$ , if $\sec \theta = - 9.5$

State in which quadrant the terminal side of the given angle lies. -218°28'

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

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is 34°48'. If the top of the dam is 2064 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

cot (-240°)

Write the expression in terms of its cofunction. -tan 42°

Solve for the requested quantity. -Find b. Round your answer to the hundredths place.

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - $\sec \theta < 0$

Perform the calculation. -180° - 23°31'27''

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ . Rationalize the denominator if necessary. If the function is undefined, say so. - $( - 8 , - 5 )$ ; find $\cot \theta$

Solve the right triangle. -B = 36.9°, c = 2.5 mm, C = 90°

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

State in which quadrant the terminal side of the given angle lies. --195.4°

Solve the right triangle. -A = 50° 28', c = 249 m , C = 90°

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - $Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find \cos B and \cot B .$ Find $\cos B$ and $\cot B$ .

Find the reference angle for the given angle. -A = -14.3°

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

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ . Rationalize the denominator if necessary. If the function is undefined, say so. - $( - 5 , \sqrt { 3 } )$ ; find $\sec \theta$

Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. $Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. b = 25 B = 35 ^ { \circ } 35 ^ { \prime }$ b = 25 $B = 35 ^ { \circ } 35 ^ { \prime }$

Convert the angle to degrees, minutes, and seconds. -246.06°

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Exam 14: Trigonometry Formerly

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - cos⁡θ\cos \thetacosθ , if sec⁡θ=−9.5\sec \theta = - 9.5secθ=−9.5

State in which quadrant the terminal side of the given angle lies. -218°28'

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

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is 34°48'. If the top of the dam is 2064 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

cot (-240°)

Write the expression in terms of its cofunction. -tan 42°

Solve for the requested quantity. -Find b. Round your answer to the hundredths place.

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - sec⁡θ<0\sec \theta < 0secθ<0

Perform the calculation. -180° - 23°31'27''

Solve the right triangle. -B = 36.9°, c = 2.5 mm, C = 90°

State in which quadrant the terminal side of the given angle lies. --195.4°

Solve the right triangle. -A = 50° 28', c = 249 m , C = 90°

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find cos⁡B\cos BcosB and cot⁡B\cot BcotB .

Find the reference angle for the given angle. -A = -14.3°

Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. b = 25 B=35∘35′B = 35 ^ { \circ } 35 ^ { \prime }B=35∘35′

Convert the angle to degrees, minutes, and seconds. -246.06°

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

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\cos \theta$ , if $\sec \theta = - 9.5$

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

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - $\sec \theta < 0$

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - $Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find \cos B and \cot B .$ Find $\cos B$ and $\cot B$ .

Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. $Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. b = 25 B = 35 ^ { \circ } 35 ^ { \prime }$ b = 25 $B = 35 ^ { \circ } 35 ^ { \prime }$