Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A)  $b = 92.1 \mathrm { feet }$ 
B)  $b = 104.5$ feet 
C)  $b = 138.5$ feet 
D)  $b = 106.07$ feet 
A)  $b = 92.1 \mathrm { feet }$ 
B)  $b = 104.5$ feet 
C)  $b = 138.5$ feet 
D)  $b = 106.07$ feet

Question 3

Without using a calculator, give the exact trigonometric function value with rational denominator.
-csc 30°

Accepted Answer

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

Question 4

$\csc \left( 1125 ^ { \circ } \right)$

Accepted Answer

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

Question 5

Use the fundamental identities to find the value of the trigonometric function.
-$\sec \beta$, if $\sin \beta = - \frac { \sqrt { 5 } } { 4 }$, with $\beta$ in quadrant III

Accepted Answer

A)  $- \frac { \sqrt { 11 } } { 4 }$ 
B)  $- 4$ 
C)  $- \frac { 4 \sqrt { 11 } } { 11 }$ 
D)  $\frac { 4 \sqrt { 11 } } { 11 }$ 
A)  $- \frac { \sqrt { 11 } } { 4 }$ 
B)  $- 4$ 
C)  $- \frac { 4 \sqrt { 11 } } { 11 }$ 
D)  $\frac { 4 \sqrt { 11 } } { 11 }$

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

Question 7

Solve the problem.
-From a boat on the lake, the angle of elevation to the top of a cliff is 12°17'. If the base of the cliff is 2716 feet from the boat, how high is the cliff (to the nearest foot)?

Accepted Answer

A) 601 ft 
B) 591 ft 
C) 594 ft 
D) 604 ft 
A) 601 ft 
B) 591 ft 
C) 594 ft 
D) 604 ft

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.
-50°

Accepted Answer

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

Question 9

Solve the problem.
-From a balloon 1033 feet high, the angle of depression to the ranger headquarters is 53°22'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Accepted Answer

A) 763 ft 
B) 758 ft 
C) 773 ft 
D) 768 ft 
A) 763 ft 
B) 758 ft 
C) 773 ft 
D) 768 ft

Question 10

Find the signs of the six trigonometric functions for the given angle.
-480°

Accepted Answer

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

Question 11

Write the expression in terms of its cofunction.
-tan 30°48'

Accepted Answer

A) cot 60°12' 
B) cot 12°59' 
C) cot 59°12' 
D) sin 59°12' 
A) cot 60°12' 
B) cot 12°59' 
C) cot 59°12' 
D) sin 59°12'

Question 12

Solve the right triangle.
-b = 1.59, c = 3.25, C = 90°

Accepted Answer

A) A = 60.7°, B = 29.3°, a = 2.8 
B) A = 63.9°, B = 26.1°, a = 3.6 
C) A = 26.1°, B = 63.9°, a = 2.8 
D) A = 60.7°, B = 29.3°, a = 3.6 
A) A = 60.7°, B = 29.3°, a = 2.8 
B) A = 63.9°, B = 26.1°, a = 3.6 
C) A = 26.1°, B = 63.9°, a = 2.8 
D) A = 60.7°, B = 29.3°, a = 3.6

Question 13

Find the exact function value if it exists.
-tan(-270°)

Accepted Answer

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

Question 14

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
- 
Find $\sin \mathrm { A }$ and $\cos \mathrm { A }$.

Accepted Answer

A)  $\sin \mathrm { A } = \frac { 4 } { 5 } ; \cos \mathrm { A } = \frac { 3 } { 5 }$ 
B)  $\sin \mathrm { A } = \frac { 4 } { 3 } ; \cos \mathrm { A } = \frac { 3 } { 4 }$ 
C)  $\sin \mathrm { A } = \frac { 5 } { 4 } ; \cos \mathrm { A } = \frac { 5 } { 3 }$ 
D)  $\sin \mathrm { A } = \frac { 3 } { 5 } ; \cos \mathrm { A } = \frac { 4 } { 5 }$ 
A)  $\sin \mathrm { A } = \frac { 4 } { 5 } ; \cos \mathrm { A } = \frac { 3 } { 5 }$ 
B)  $\sin \mathrm { A } = \frac { 4 } { 3 } ; \cos \mathrm { A } = \frac { 3 } { 4 }$ 
C)  $\sin \mathrm { A } = \frac { 5 } { 4 } ; \cos \mathrm { A } = \frac { 5 } { 3 }$ 
D)  $\sin \mathrm { A } = \frac { 3 } { 5 } ; \cos \mathrm { A } = \frac { 4 } { 5 }$

Question 15

Find the signs of the six trigonometric functions for the given angle.
--10°

Accepted Answer

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

Question 16

Use a calculator to find the function value to four decimal places.
-sin (-10°37')

Accepted Answer

A) -0.1673 
B) -0.18 
C) -0.163 
D) -0.1842 
A) -0.1673 
B) -0.18 
C) -0.163 
D) -0.1842

Question 17

Use a calculator to find the function value to four decimal places.
-cos 321°10'

Accepted Answer

A) 0.979 
B) 0.3895 
C) 0.779 
D) 0.2895 
A) 0.979 
B) 0.3895 
C) 0.779 
D) 0.2895

Question 18

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

$a = 6$
$\mathrm { A } = 56 ^ { \circ } 42 ^ { \prime }$

Accepted Answer

A)  $B = 33 ^ { \circ } 18 ^ { \prime } , c = 7.2 , b = 3.9$ 
B)  $B = 33 ^ { \circ } 18 ^ { \prime } , c = 7.2 , b = 10.8$ 
C)  $B = 33 ^ { \circ } 18 ^ { \prime } , \mathrm { c } = 7.2 , \mathrm {~b} = 10.9$ 
D)  $B = 33 ^ { \circ } 18 ^ { \prime } , \mathrm { c } = 10.9 , \mathrm {~b} = 7.2$ 
A)  $B = 33 ^ { \circ } 18 ^ { \prime } , c = 7.2 , b = 3.9$ 
B)  $B = 33 ^ { \circ } 18 ^ { \prime } , c = 7.2 , b = 10.8$ 
C)  $B = 33 ^ { \circ } 18 ^ { \prime } , \mathrm { c } = 7.2 , \mathrm {~b} = 10.9$ 
D)  $B = 33 ^ { \circ } 18 ^ { \prime } , \mathrm { c } = 10.9 , \mathrm {~b} = 7.2$

Question 19

Find the angle of smallest possible positive measure coterminal with the given angle.
-1326°

Accepted Answer

A) 246° 
B) 606° 
C) 156° 
D) 66° 
A) 246° 
B) 606° 
C) 156° 
D) 66°

Question 20

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

Accepted Answer

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

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

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

Without using a calculator, give the exact trigonometric function value with rational denominator. -csc 30°

$\csc \left( 1125 ^ { \circ } \right)$

Use the fundamental identities to find the value of the trigonometric function. - $\sec \beta$ , if $\sin \beta = - \frac { \sqrt { 5 } } { 4 }$ , with $\beta$ in quadrant III

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

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is 12°17'. If the base of the cliff is 2716 feet from the boat, how high is the cliff (to the nearest foot)?

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. -50°

Solve the problem. -From a balloon 1033 feet high, the angle of depression to the ranger headquarters is 53°22'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Find the signs of the six trigonometric functions for the given angle. -480°

Write the expression in terms of its cofunction. -tan 30°48'

Solve the right triangle. -b = 1.59, c = 3.25, C = 90°

Find the exact function value if it exists. -tan(-270°)

Find the signs of the six trigonometric functions for the given angle. --10°

Use a calculator to find the function value to four decimal places. -sin (-10°37')

Use a calculator to find the function value to four decimal places. -cos 321°10'

Find the angle of smallest possible positive measure coterminal with the given angle. -1326°

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

The Art of Problem Solving

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Exam 14: Trigonometry Formerly

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. - III, rx\text { III, } \frac{r}{x} III, xr​

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

Without using a calculator, give the exact trigonometric function value with rational denominator. -csc 30°

csc⁡(1125∘)\csc \left( 1125 ^ { \circ } \right)csc(1125∘)

Use the fundamental identities to find the value of the trigonometric function. - sec⁡β\sec \betasecβ , if sin⁡β=−54\sin \beta = - \frac { \sqrt { 5 } } { 4 }sinβ=−45​​ , with β\betaβ in quadrant III

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - tan⁡θ>0\tan \theta > 0tanθ>0 and sin⁡θ<0\sin \theta < 0sinθ<0

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is 12°17'. If the base of the cliff is 2716 feet from the boat, how high is the cliff (to the nearest foot)?

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. -50°

Solve the problem. -From a balloon 1033 feet high, the angle of depression to the ranger headquarters is 53°22'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Find the signs of the six trigonometric functions for the given angle. -480°

Write the expression in terms of its cofunction. -tan 30°48'

Solve the right triangle. -b = 1.59, c = 3.25, C = 90°

Find the exact function value if it exists. -tan(-270°)

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find sin⁡A\sin \mathrm { A }sinA and cos⁡A\cos \mathrm { A }cosA .

Find the signs of the six trigonometric functions for the given angle. --10°

Use a calculator to find the function value to four decimal places. -sin (-10°37')

Use a calculator to find the function value to four decimal places. -cos 321°10'

Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. a=6a = 6a=6 A=56∘42′\mathrm { A } = 56 ^ { \circ } 42 ^ { \prime }A=56∘42′

Find the angle of smallest possible positive measure coterminal with the given angle. -1326°

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - sin⁡θ>0\sin \theta > 0sinθ>0 and cos⁡θ<0\cos \theta < 0cosθ<0

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

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

$\csc \left( 1125 ^ { \circ } \right)$

Use the fundamental identities to find the value of the trigonometric function. - $\sec \beta$ , if $\sin \beta = - \frac { \sqrt { 5 } } { 4 }$ , with $\beta$ in quadrant III

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

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