Question 1

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-53°58'12''

Accepted Answer

A) 53.98 
B) 53.93 
C) 53.97 
D) 54.03 
A) 53.98 
B) 53.93 
C) 53.97 
D) 54.03

Question 2

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

Accepted Answer

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

Question 3

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.
-130°

Accepted Answer

A)  $490^{\circ} \text { and }-230^{\circ}$
  
B)  $490 ^ { \circ }$ and $- 230 ^ { \circ }$
  
C)  $310 ^ { \circ }$ and $- 50 ^ { \circ }$
  
D)  $310 ^ { \circ }$ and $- 50 ^ { \circ }$
  
A)  $490^{\circ} \text { and }-230^{\circ}$
  
B)  $490 ^ { \circ }$ and $- 230 ^ { \circ }$
  
C)  $310 ^ { \circ }$ and $- 50 ^ { \circ }$
  
D)  $310 ^ { \circ }$ and $- 50 ^ { \circ }$

Question 4

Find the reference angle for the given angle.
-A = 259.2°

Accepted Answer

A) 169.2° 
B) 10.8° 
C) 79.2° 
D) 100.8° 
A) 169.2° 
B) 10.8° 
C) 79.2° 
D) 100.8°

Question 5

Solve for the requested quantity.
-Find all missing sides and angles. Round to the nearest tenth.

$\mathrm { C } = 40$
$B = 16 ^ { \circ } 27 { } ^ { \prime }$

Accepted Answer

A)  $\mathrm { A } = 73 ^ { \circ } 33 ^ { \prime } , \mathrm { a } = 38.4 , \mathrm {~b} = 11.3$ 
B)  $\mathrm { A } = 73 ^ { \circ } 33 ^ { \prime } , \mathrm { a } = 11.2 , \mathrm {~b} = 38.4$ 
C)  $\mathrm { A } = 73 ^ { \circ } 33 ^ { \prime } , \mathrm { a } = 11.3 , \mathrm {~b} = 38.4$ 
D)  $\mathrm { A } = 73 ^ { \circ } 33 ^ { \prime } , \mathrm { a } = 11.3 , \mathrm {~b} = 11.8$ 
A)  $\mathrm { A } = 73 ^ { \circ } 33 ^ { \prime } , \mathrm { a } = 38.4 , \mathrm {~b} = 11.3$ 
B)  $\mathrm { A } = 73 ^ { \circ } 33 ^ { \prime } , \mathrm { a } = 11.2 , \mathrm {~b} = 38.4$ 
C)  $\mathrm { A } = 73 ^ { \circ } 33 ^ { \prime } , \mathrm { a } = 11.3 , \mathrm {~b} = 38.4$ 
D)  $\mathrm { A } = 73 ^ { \circ } 33 ^ { \prime } , \mathrm { a } = 11.3 , \mathrm {~b} = 11.8$

Question 6

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

Accepted Answer

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

Question 7

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-356°49'41''

Accepted Answer

A) 356.79 
B) 356.84 
C) 356.89 
D) 356.83 
A) 356.79 
B) 356.84 
C) 356.89 
D) 356.83

Question 8

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.
-20°

Accepted Answer

A)  $380 ^ { \circ }$ and $- 340 ^ { \circ }$
  
B)  $2380 ^ { \circ }$ and $- 340 ^ { \circ }$
  
C)  $200 ^ { \circ }$ and $- 160 ^ { \circ }$
  
D)  $200 ^ { \circ }$ and $- 160 ^ { \circ }$
  
A)  $380 ^ { \circ }$ and $- 340 ^ { \circ }$
  
B)  $2380 ^ { \circ }$ and $- 340 ^ { \circ }$
  
C)  $200 ^ { \circ }$ and $- 160 ^ { \circ }$
  
D)  $200 ^ { \circ }$ and $- 160 ^ { \circ }$

Question 9

A contractor needs to know the height of a building to estimate the cost of a job. From a point 83 feet away from the base of the building, the angle of elevation to the top of the building is found to
Be 44° 10'. Find the height of the building. Round your answer to the hundredths place.

Accepted Answer

A) 84.85 ft 
B) 79.09 ft 
C) 83.52 ft 
D) 80.62ft 
A) 84.85 ft 
B) 79.09 ft 
C) 83.52 ft 
D) 80.62ft

Question 10

Find the reference angle for the given angle.
-A = 84°

Accepted Answer

A) 174° 
B) 96° 
C) 84° 
D) 6° 
A) 174° 
B) 96° 
C) 84° 
D) 6°

Question 11

Perform the calculation.
-90° - 44°25'

Accepted Answer

A) 46°25' 
B) 46°35' 
C) 45°35' 
D) 45°25' 
A) 46°25' 
B) 46°35' 
C) 45°35' 
D) 45°25'

Question 12

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement.
-sec ϴ= 8.094

Accepted Answer

A) -7.04° 
B) 7.10° 
C) 7.04° 
D) 82.90° 
A) -7.04° 
B) 7.10° 
C) 7.04° 
D) 82.90°

Question 13

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
--86°

Accepted Answer

A) -86° + 2n · 360° 
B) -86° + n · 180° 
C) -86° + n · 360° 
D) -86° - n · 180° 
A) -86° + 2n · 360° 
B) -86° + n · 180° 
C) -86° + n · 360° 
D) -86° - n · 180°

Question 14

Find the signs of the six trigonometric functions for the given angle.
-330°

Accepted Answer

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

Question 15

In one area, the lowest angle of elevation of the sun in winter is 23° 45'. Find the minimum distance x that a plant needing full sun can be placed from a fence that is 5 feet high. Round your answer to
The tenths place.

Accepted Answer

A)  $14.8 \mathrm { ft }$ 
B)  $11 \mathrm { ft }$ 
C)  $11.4 \mathrm { ft }$ 
D)  $11.6 \mathrm { ft }$ 
A)  $14.8 \mathrm { ft }$ 
B)  $11 \mathrm { ft }$ 
C)  $11.4 \mathrm { ft }$ 
D)  $11.6 \mathrm { ft }$

Question 16

Use the fundamental identities to find the value of the trigonometric function.
-$\tan \alpha$, if $\sec \alpha = \frac { 9 } { 4 }$, with $\alpha$ in quadrant IV

Accepted Answer

A)  $- \frac { \sqrt { 65 } } { 4 }$ 
B)  $- \frac { 9 } { 4 }$ 
C)  $- \sqrt { 65 }$ 
D)  $- \frac { \sqrt { 65 } } { 9 }$ 
A)  $- \frac { \sqrt { 65 } } { 4 }$ 
B)  $- \frac { 9 } { 4 }$ 
C)  $- \sqrt { 65 }$ 
D)  $- \frac { \sqrt { 65 } } { 9 }$

Question 17

Find the signs of the six trigonometric functions for the given angle.
-19°

Accepted Answer

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

Question 18

Use the fundamental identities to find the value of the trigonometric function.
-$\cos \omega$, if $\tan \omega = - \frac { 2 } { 7 }$ and $\sin \omega > 0$

Accepted Answer

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

Question 19

Write the expression in terms of its cofunction.
-csc 63°

Accepted Answer

A) sin 63° 
B) sec 63° 
C) sec 27° 
D) sec 153° 
A) sin 63° 
B) sec 63° 
C) sec 27° 
D) sec 153°

Question 20

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

Accepted Answer

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

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -53°58'12''

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

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. -130°

Find the reference angle for the given angle. -A = 259.2°

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

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -356°49'41''

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. -20°

A contractor needs to know the height of a building to estimate the cost of a job. From a point 83 feet away from the base of the building, the angle of elevation to the top of the building is found to Be 44° 10'. Find the height of the building. Round your answer to the hundredths place.

Find the reference angle for the given angle. -A = 84°

Perform the calculation. -90° - 44°25'

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -sec ϴ= 8.094

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. --86°

Find the signs of the six trigonometric functions for the given angle. -330°

In one area, the lowest angle of elevation of the sun in winter is 23° 45'. Find the minimum distance x that a plant needing full sun can be placed from a fence that is 5 feet high. Round your answer to The tenths place.

Use the fundamental identities to find the value of the trigonometric function. - $\tan \alpha$ , if $\sec \alpha = \frac { 9 } { 4 }$ , with $\alpha$ in quadrant IV

Find the signs of the six trigonometric functions for the given angle. -19°

Use the fundamental identities to find the value of the trigonometric function. - $\cos \omega$ , if $\tan \omega = - \frac { 2 } { 7 }$ and $\sin \omega > 0$

Write the expression in terms of its cofunction. -csc 63°

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

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Exam 14: Trigonometry Formerly