Deck 7: Additional Topics in Trigonometry

Question 1

Solve the triangle.
$\mathrm { A } = 26 ^ { \circ } , \mathrm { B } = 51 ^ { \circ } , \mathrm { c } = 22$

A) $\mathrm { C } = 103 ^ { \circ } , \mathrm { a } = 9.9 , \mathrm {~b} = 17.5$
B) $\mathrm { C } = 103 ^ { \circ } , \mathrm { a } = 17.5 , \mathrm {~b} = 9.9$
C) $\mathrm { C } = 103 ^ { \circ } , \mathrm { a } = 48.9 , \mathrm {~b} = 27.6$
D) $C = 97 ^ { \circ } , a = 9.7 , b = 17.2$

Answer 1

A

Question 2

Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
$$\mathrm { C } = 35 ^ { \circ } , \mathrm { a } = 18.7 , \mathrm { c } = 16.1$$

A) $\mathrm { A } _ { 1 } = 42 ^ { \circ } , \mathrm { B } _ { 1 } = 103 ^ { \circ } , \mathrm { b } _ { 1 } = 27.4$ ;
$\mathrm { A } _ { 2 } = 7 ^ { \circ } , \mathrm { B } _ { 2 } = 138 ^ { \circ } , \mathrm { b } _ { 2 } = 3.4$

B) $\mathrm { A } _ { 1 } = 103 ^ { \circ } , \mathrm { B } _ { 1 } = 42 ^ { \circ } , \mathrm { b } _ { 1 } = 27.4$ ;
$$\mathrm { A } _ { 2 } = 138 ^ { \circ } , \mathrm { B } _ { 2 } = 7 ^ { \circ } , \mathrm { b } _ { 2 } = 3.4$$

C) $\mathrm { A } = 42 ^ { \circ } , \mathrm { B } = 103 ^ { \circ } , \mathrm { b } = 27.4$
D) no triangle

Answer 2

A

Question 3

Solve Applied Problems Using the Law of Sines
Two tracking stations are on the equator 130 miles apart. A weather balloon is located on a bearing of $\mathrm { N } 42 ^ { \circ } \mathrm { E }$ from the western station and on a bearing of N22 $\mathrm { W }$ from the eastern station. How far is the balloon from the western station? Round to the nearest mile.

A) 134 miles
B) 143 miles
C) 107 miles
D) 98 miles

Answer 3

A

Question 4

Solve the triangle.

A) $\mathrm { C } = 35 ^ { \circ } , \mathrm { a } = 18.13 , \mathrm { c } = 11.47$
B) $\mathrm { C } = 35 ^ { \circ } , \mathrm { a } = 11.47 , \mathrm { c } = 18.13$
C) $\mathrm { C } = 40 ^ { \circ } , \mathrm { a } = 18.13 , \mathrm { c } = 11.47$
D) $\mathrm { C } = 30 ^ { \circ } , \mathrm { a } = 11.47 , \mathrm { c } = 18.13$ Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.

Question 5

Find the Area of an Oblique Triangle Using the Sine Function
$\mathrm { C } = 105 ^ { \circ } , \mathrm { a } = 1$ yards, $\mathrm { b } = 5$ yards

A) 2 square yards
B) 5 square yards
C) 10 square yards
D) 1 square yards

Question 6

Solve Applied Problems Using the Law of Sines
A surveyor standing 50 meters from the base of a building measures the angle to the top of the building and finds it to be $37 ^ { \circ }$ . The surveyor then measures the angle to the top of the radio tower on the building and finds that it is $47 ^ { \circ }$ . How tall is the radio tower?

A) $15.94$ meters
B) $6.48$ meters
C) $5.83$ meters
D) $8.82$ meters

Question 7

Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
$$\mathrm { A } = 85 ^ { \circ } , \mathrm { a } = 4 , \mathrm {~b} = 5$$

A) no triangle
B) $B = 44 ^ { \circ } , C = 51 ^ { \circ } , \mathrm { C } = 13$
C) $\mathrm { A } = 43 ^ { \circ } , \mathrm { C } = 52 ^ { \circ } , \mathrm { c } = 9$
D) $B = 42 ^ { \circ } , C = 53 ^ { \circ } , \mathrm { C } = 11$

Question 8

Find the Area of an Oblique Triangle Using the Sine Function
$\mathrm { B } = 25 ^ { \circ } , \mathrm { a } = 3$ feet, $\mathrm { c } = 7$ feet

A) 4 square feet
B) 9 square feet
C) 18 square feet
D) 10 square feet

Question 9

Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
$$\mathrm { B } = 112 ^ { \circ } , \mathrm { b } = 4 , \mathrm { a } = 25$$

A) no triangle
B) $\mathrm { A } = 57 ^ { \circ } , \mathrm { C } = 12 ^ { \circ } , \mathrm { c } = 33$
C) $\mathrm { A } = 56 ^ { \circ } , \mathrm { C } = 12 ^ { \circ } , \mathrm { c } = 29$
D) $\mathrm { A } = 55 ^ { \circ } , \mathrm { C } = 12 ^ { \circ } , \mathrm { c } = 31$

Question 10

Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
$$\mathrm { B } = 20 ^ { \circ } , \mathrm { b } = 11.0 , \mathrm { a } = 16.08$$

A) $\mathrm { A } _ { 1 } = 30 ^ { \circ } , \mathrm { C } _ { 1 } = 130 ^ { \circ } , \mathrm { c } _ { 1 } = 24.6$ ;
$\mathrm{A}_{2}=150^{\circ}, \mathrm{C}_{2}=10^{\circ}, \mathrm{c}_{2}=5.6$

B) $\mathrm { A } = 30 ^ { \circ } , \mathrm { C } = 130 ^ { \circ } , \mathrm { c } = 24.6$

C) $\mathrm { A } = 150 ^ { \circ } , \mathrm { C } = 10 ^ { \circ } , \mathrm { c } = 5.6$
D) no triangle

Question 11

Solve Applied Problems Using the Law of Sines
To find the distance $\mathrm { AB }$ across a river, a distance $\mathrm { BC }$ of $293 \mathrm {~m}$ is laid off on one side of the river. It is found that $\mathrm { B } = 110.8 ^ { \circ }$ and $\mathrm { C } = 17.9 ^ { \circ }$ . Find $\mathrm { AB }$ . Round to the nearest meter.

A) 115 meters
B) 118 meters
C) 90 meters
D) 87 meters

Question 12

Find the Area of an Oblique Triangle Using the Sine Function
$\mathrm { A } = 26 ^ { \circ } , \mathrm { b } = 17$ meters, $\mathrm { c } = 5$ meters

A) 19 square meters
B) 10 square meters
C) 38 square meters
D) 40 square meters

Question 13

Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
$$\mathrm { B } = 45 ^ { \circ } , \mathrm { b } = 4 , \mathrm { a } = 34$$

A) no triangle
B) $\mathrm { A } = 41 ^ { \circ } , \mathrm { C } = 93 ^ { \circ } , \mathrm { c } = 35$
C) $\mathrm { A } = 43 ^ { \circ } , \mathrm { C } = 91 ^ { \circ } , \mathrm { c } = 38$
D) $\mathrm { A } = 44 ^ { \circ } , \mathrm { C } = 92 ^ { \circ } , \mathrm { C } = 39.5$

Question 14

Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
$\mathrm { B } = 41 ^ { \circ } , \mathrm { a } = 4 , \mathrm {~b} = 3$

A) $\mathrm { A } _ { 1 } = 61 ^ { \circ } , \mathrm { C } _ { 1 } = 78 ^ { \circ } , \mathrm { C } _ { 1 } = 4.5$ ;
$\mathrm { A } _ { 2 } = 119 ^ { \circ } , \mathrm { C } _ { 2 } = 20 ^ { \circ } , \mathrm { c } _ { 2 } = 1.6$

B) $\mathrm { A } _ { 1 } = 61 ^ { \circ } , \mathrm { C } _ { 1 } = 78 ^ { \circ } , \mathrm { C } _ { 1 } = 0.1$ ;
$\mathrm { A } _ { 2 } = 119 ^ { \circ } , \mathrm { C } _ { 2 } = 20 ^ { \circ } , \mathrm { C } _ { 2 } = 0.1$
C) $\mathrm { A } = 29 ^ { \circ } , \mathrm { C } = 110 ^ { \circ } , \mathrm { c } = 5.7$
D) no triangle

Question 15

Solve the triangle.

A) $\mathrm { B } = 65 ^ { \circ } , \mathrm { a } = 3.9 , \mathrm { c } = 5.18$
B) $B = 65 ^ { \circ } , a = 5.18 , c = 3.9$
C) $B = 70 ^ { \circ } , a = 3.9 , c = 5.18$
D) $\mathrm { B } = 60 ^ { \circ } , \mathrm { a } = 5.18 , \mathrm { c } = 3.9$

Question 16

Solve the triangle.
$$\begin{array} { l } B = 27 ^ { \circ } \\C = 114 ^ { \circ } \\b = 29\end{array}$$

A) $\mathrm { A } = 39 ^ { \circ } , \mathrm { a } = 40.2 , \mathrm { c } = 58.4$
B) $\mathrm { A } = 37 ^ { \circ } , \mathrm { a } = 58.4 , \mathrm { c } = 40.2$
C) $\mathrm { A } = 39 ^ { \circ } , \mathrm { a } = 42.2 , \mathrm { c } = 60.4$
D) $\mathrm { A } = 37 ^ { \circ } , \mathrm { a } = 60.4 , \mathrm { c } = 42.2$

Question 17

Use the Law of Sines to Solve, if Possible, the Triangle or Triangles in the Ambiguous Case
$$\mathrm { A } = 30 ^ { \circ } , \mathrm { a } = 11 , \mathrm {~b} = 22$$

A) $\mathrm { B } = 90 ^ { \circ } , \mathrm { C } = 60 ^ { \circ } , \mathrm { c } = 19.1$
B) $B = 60 ^ { \circ } , C = 90 ^ { \circ } , c = 19.1$
C) $B = 60 ^ { \circ } , C = 60 ^ { \circ } , \mathrm { C } = 19.1$
D) no triangle

Question 18

Solve the triangle.
$\mathrm { A } = 11.2 ^ { \circ } , \mathrm { C } = 131.6 ^ { \circ } , \mathrm { a } = 80.4$

A) B $= 37.2 ^ { \circ } , \mathrm { b } = 250.3 , \mathrm { c } = 309.5$
B) $B = 37.2 ^ { \circ } , b = 309.5 , c = 250.3$
C) $\mathrm { B } = 37.2 ^ { \circ } , \mathrm { b } = 25.8 , \mathrm { c } = 21$
D) $\mathrm { B } = 36.8 ^ { \circ } , \mathrm { b } = 248 , \mathrm { c } = 309.5$

Question 19

Solve the triangle.
$$\begin{array} { l } \mathrm { A } = 47 ^ { \circ } \\\mathrm { B } = 42 ^ { \circ } \\\mathrm { a } = 45.2\end{array}$$

A) $\mathrm { C } = 91 ^ { \circ } , \mathrm { b } = 41.4 , \mathrm { c } = 61.8$
B) $\mathrm { C } = 92 ^ { \circ } , \mathrm { b } = 41.4 , \mathrm { c } = 61.8$
C) $\mathrm { C } = 91 ^ { \circ } , \mathrm { b } = 61.8 , \mathrm { c } = 41.4$
D) $\mathrm { C } = 92 ^ { \circ } , \mathrm { b } = 61.8 , \mathrm { c } = 41.4$

Question 20

Find the Area of an Oblique Triangle Using the Sine Function
$\mathrm { A } = 27 ^ { \circ } , \mathrm { b } = 14$ inches, $\mathrm { c } = 5$ inches

A) 16 square inches
B) 31 square inches
C) 14 square inches
D) 33 square inches

Question 21

Solve Applied Problems Using the Law of Cosines
A painter needs to cover a triangular region 61 meters by 68 meters by 72 meters. A can of paint covers 70 square meters. How many cans will be needed?

A) 28 cans
B) 314 cans
C) 14 cans
D) 3 cans

Question 22

Solve Applied Problems Using the Law of Cosines
Two sailboats leave a harbor in the Bahamas at the same time. The first sails at $21 \mathrm { mph }$ in a direction $350 ^ { \circ }$ . The second sails at $33 \mathrm { mph }$ in a direction $220 ^ { \circ }$ . Assuming that both boats maintain speed and heading, after 4 hours, how far apart are the boats?

A) $196.8$ miles
B) $125.6$ miles
C) $142.7$ miles
D) $171.9$ miles

Question 23

The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
$$\mathrm { a } = 7 , \mathrm {~b} = 14 , \mathrm { c } = 16$$

A) $\mathrm { A } = 26 ^ { \circ } , \mathrm { B } = 61 ^ { \circ } , \mathrm { C } = 93 ^ { \circ }$
B) $\mathrm { A } = 28 ^ { \circ } , \mathrm { B } = 59 ^ { \circ } , \mathrm { C } = 93 ^ { \circ }$
C) $\mathrm { A } = 24 ^ { \circ } , \mathrm { B } = 61 ^ { \circ } , \mathrm { C } = 95 ^ { \circ }$
D) no triangle

Question 24

The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
$$a = 8 , b = 11 , C = 123 ^ { \circ }$$

A) $\mathrm { c } = 16.8 , \mathrm {~A} = 24 ^ { \circ } , \mathrm { B } = 33 ^ { \circ }$
B) $\mathrm { c } = 19.7 , \mathrm {~A} = 26 ^ { \circ } , \mathrm { B } = 31 ^ { \circ }$
C) $\mathrm { c } = 22.6 , \mathrm {~A} = 22 ^ { \circ } , \mathrm { B } = 35 ^ { \circ }$
D) no triangle

Question 25

The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles

A) $\mathrm { A } = 109 ^ { \circ } , \mathrm { B } = 39 ^ { \circ } , \mathrm { C } = 32 ^ { \circ }$
B) $\mathrm { A } = 39 ^ { \circ } , \mathrm { B } = 109 ^ { \circ } , \mathrm { C } = 32 ^ { \circ }$
C) $A = 109 ^ { \circ } , \mathrm { B } = 32 ^ { \circ } , \mathrm { C } = 39 ^ { \circ }$
D) $\mathrm { A } = 39 ^ { \circ } , \mathrm { B } = 32 ^ { \circ } , \mathrm { C } = 109 ^ { \circ }$

Question 26

The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles

A) $\mathrm { A } = 59 ^ { \circ } , \mathrm { B } = 35 ^ { \circ } , \mathrm { C } = 86 ^ { \circ }$
B) $\mathrm { A } = 35 ^ { \circ } , \mathrm { B } = 59 ^ { \circ } , \mathrm { C } = 86 ^ { \circ }$
C) $\mathrm { A } = 59 ^ { \circ } , \mathrm { B } = 86 ^ { \circ } , \mathrm { C } = 35 ^ { \circ }$
D) $\mathrm { A } = 35 ^ { \circ } , \mathrm { B } = 86 ^ { \circ } , \mathrm { C } = 59 ^ { \circ }$

Question 27

Solve Applied Problems Using the Law of Cosines
Two airplanes leave an airport at the same time, one going northwest (bearing $135 ^ { \circ }$ ) at $422 \mathrm { mph }$ and the other going east at $347 \mathrm { mph }$ . How far apart are the planes after 2 hours (to the nearest mile)?

A) 1422 miles
B) 711 miles
C) 1184 miles
D) 1268 miles

Question 28

Solve Applied Problems Using the Law of Cosines
The distance from home plate to dead center field in Sun Devil Stadium is 406 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center field?

A) $348.2$ feet
B) $383.5$ feet
C) $473.9$ feet
D) $331.1$ feet

Question 29

Additional Concepts

A) $17.71$
B) $6.52$
C) $6.3$
D) $9.17$

Question 30

The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
$$\mathrm { a } = 8 , \mathrm { c } = 8 , \mathrm {~B} = 128 ^ { \circ }$$

A) $\mathrm { b } = 14.4 , \mathrm {~A} = 26 ^ { \circ } , \mathrm { C } = 26 ^ { \circ }$
B) $\mathrm { b } = 17.3 , \mathrm {~A} = 28 ^ { \circ } , \mathrm { C } = 24 ^ { \circ }$
C) $\mathrm { b } = 20.2 , \mathrm {~A} = 24 ^ { \circ } , \mathrm { C } = 28 ^ { \circ }$
D) no triangle

Question 31

The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
$$a = 9 , b = 9 , c = 8$$

A) $\mathrm { A } = 64 ^ { \circ } , \mathrm { B } = 64 ^ { \circ } , \mathrm { C } = 52 ^ { \circ }$
B) $\mathrm { A } = 65 ^ { \circ } , \mathrm { B } = 65 ^ { \circ } , \mathrm { C } = 50 ^ { \circ }$
C) $\mathrm { A } = 52 ^ { \circ } , \mathrm { B } = 64 ^ { \circ } , \mathrm { C } = 64 ^ { \circ }$
D) $\mathrm { A } = 64 ^ { \circ } , \mathrm { B } = 52 ^ { \circ } , \mathrm { C } = 64 ^ { \circ }$

Question 32

Solve Applied Problems Using the Law of Cosines
A plane flying a straight course observes a mountain at a bearing of $31.7 ^ { \circ }$ to the right of its course. At that time the plane is 8 kilometers from the mountain. A short time later, the bearing to the mountain becomes $41.7 ^ { \circ }$ . How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a $\mathrm { km } ) ?$

A) $6.3$ kilometers
B) $10.1$ kilometers
C) $11.4$ kilometers
D) $4.2$ kilometers

Question 33

The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
$$b = 6 , c = 10 , A = 119 ^ { \circ }$$

A) $a = 13.9 , B = 22 ^ { \circ } , C = 39 ^ { \circ }$
B) $\mathrm { a } = 16.8 , \mathrm {~B} = 24 ^ { \circ } , \mathrm { C } = 37 ^ { \circ }$
C) $\mathrm { a } = 19.7 , \mathrm {~B} = 20 ^ { \circ } , \mathrm { C } = 41 ^ { \circ }$
D) no triangle

Question 34

The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
$$a = 4 , c = 2 , B = 90 ^ { \circ }$$

A) $\mathrm { b } = 4.5 , \mathrm {~A} = 63 ^ { \circ } , \mathrm { C } = 27 ^ { \circ }$
B) $\mathrm { b } = 4.5 , \mathrm {~A} = 27 ^ { \circ } , \mathrm { C } = 63 ^ { \circ }$
C) $\mathrm { b } = 5.5 , \mathrm {~A} = 63 ^ { \circ } , \mathrm { C } = 27 ^ { \circ }$
D) $b = 3.5 , \mathrm {~A} = 27 ^ { \circ } , \mathrm { C } = 63 ^ { \circ }$

Question 35

The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
$$\mathrm { b } = 4 , \mathrm { c } = 6 , \mathrm {~A} = 80 ^ { \circ }$$

A) $\mathrm { a } = 6.6 , \mathrm {~B} = 37 ^ { \circ } , \mathrm { C } = 63 ^ { \circ }$
B) $a = 6.6 , \mathrm {~B} = 63 ^ { \circ } , \mathrm { C } = 37 ^ { \circ }$
C) $a = 7.6 , B = 37 ^ { \circ } , C = 63 ^ { \circ }$
D) $a = 5.6 , B = 63 ^ { \circ } , C = 37 ^ { \circ }$

Question 36

Additional Concepts

A) $7.08$
B) $2.06$
C) $9.28$
D) $3.54$

Question 37

Solve Applied Problems Using the Law of Cosines
Two points $A$ and $B$ are on opposite sides of a building. A surveyor selects a third point $C$ to place a transit. Point $\mathrm { C }$ is 54 feet from point $\mathrm { A }$ and 72 feet from point $B$ . The angle $A C B$ is $60 ^ { \circ }$ . How far apart are points $A$ and $B$ ?

A) $64.9$ feet
B) $109.5$ feet
C) $78.5$ feet
D) $100.2$ feet

Question 38

Solve Applied Problems Using the Law of Sines
A guy wire to a tower makes a $74 ^ { \circ }$ angle with level ground. At a point $37 \mathrm { ft }$ farther from the tower than the wire but on the same side as the base of the wire, the angle of elevation to the top of the tower is $33 ^ { \circ }$ . Find the length of the wire (to the nearest foot).

A) 31 feet
B) 36 feet
C) 62 feet
D) 67 feet

Question 39

The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
$$a = 8 , b = 6 , c = 4$$

A) $\mathrm { A } = 104 ^ { \circ } , \mathrm { B } = 47 ^ { \circ } , \mathrm { C } = 29 ^ { \circ }$
B) $\mathrm { A } = 47 ^ { \circ } , \mathrm { B } = 104 ^ { \circ } , \mathrm { C } = 29 ^ { \circ }$
C) $\mathrm { A } = 104 ^ { \circ } , \mathrm { B } = 29 ^ { \circ } , \mathrm { C } = 47 ^ { \circ }$
D) $\mathrm { A } = 47 ^ { \circ } , \mathrm { B } = 29 ^ { \circ } , \mathrm { C } = 104 ^ { \circ }$

Question 40

Use Heron's Formula to Find the Area of a Triangle
$a = 20$ yards, $b = 13$ yards, $c = 17$ yards

A) 110 square yards
B) 113 square yards
C) 116 square yards
D) 119 square yards

Question 41

Convert a Point from Polar to Rectangular Coordinates
$$\left( 3 , - 135 ^ { \circ } \right)$$

A) $\left( \frac { - 3 \sqrt { 2 } } { 2 } , \frac { - 3 \sqrt { 2 } } { 2 } \right)$
B) $\left( \frac { - 3 \sqrt { 2 } } { 2 } , \frac { 3 \sqrt { 2 } } { 2 } \right)$
C) $\left( \frac { 3 \sqrt { 2 } } { 2 } , \frac { 3 \sqrt { 2 } } { 2 } \right)$
D) $\left( \frac { 3 \sqrt { 2 } } { 2 } , \frac { - 3 \sqrt { 2 } } { 2 } \right)$

Question 42

Polar Coordinates
1 Plot Points in the Polar Coordinate System
Match the point in polar coordinates with either A, B, C, or D on the graph.
$\left(-2,-135^{\circ}\right)$

A)

B)
C)

D)

Question 43

Convert a Point from Polar to Rectangular Coordinates
$\left( - 3 , - 90 ^ { \circ } \right)$

A) $( 0,3 )$
В) $( 3,0 )$
C) $( 0 , - 3 )$
D) $( - 3,0 )$

Question 44

Polar Coordinates
1 Plot Points in the Polar Coordinate System
Match the point in polar coordinates with either A, B, C, or D on the graph.
$$\left( 4 , \frac { - 3 \pi } { 4 } \right)$$

A)

B)


C)

D)

Question 45

Solve the problem.
$\left( 4 , \frac { \pi } { 3 } \right) , \mathrm { r } < 0$ and $0 < \theta < 2 \pi$

A) $\left( - 4 , \frac { 4 } { 3 } \pi \right)$
B) $\left( - 4 , - \frac { 2 } { 3 } \pi \right)$
C) $\left( - 4 , \frac { 7 } { 3 } \pi \right)$
D) $\left( - 4 , - \frac { 5 } { 3 } \pi \right)$

Question 46

Solve the problem.
$\left( 2 , \frac { \pi } { 6 } \right) , r > 0$ and $2 \pi < \theta < 4 \pi$

A) $\left( 2 , \frac { 13 } { 6 } \pi \right)$
B) $\left( 2 , - \frac { 11 } { 6 } \pi \right)$
C) $\left( 2 , \frac { 7 } { 6 } \pi \right)$
D) $\left( 2 , - \frac { 5 } { 6 } \pi \right)$

Question 47

Solve the problem.
$\left( 6,170 ^ { \circ } \right)$

A) $( 6,530 ) ^ { \circ }$
B) $( 6,350 ) ^ { \circ }$
C) $( - 6,530 ) ^ { \circ }$
D) $( - 6,260 ) ^ { \circ }$

Question 48

Convert a Point from Polar to Rectangular Coordinates
$$\left( - 3,120 ^ { \circ } \right)$$

A) $\left( \frac { 3 } { 2 } , \frac { - 3 \sqrt { 3 } } { 2 } \right)$
B) $\left( - \frac { 3 } { 2 } , \frac { - 3 \sqrt { 3 } } { 2 } \right)$
C) $\left( \frac { 3 } { 2 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$
D) $\left( - \frac { 3 } { 2 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$

Question 49

Solve the problem.
$\left( 9 , \frac { \pi } { 3 } \right) , \mathrm { r } < 0$ and $2 \pi < \theta < 4 \pi$

A) $\left( - 9 , \frac { 10 } { 3 } \pi \right)$
B) $\left( - 9 , - \frac { 8 } { 3 } \pi \right)$
C) $\left( - 9 , \frac { 7 } { 3 } \pi \right)$
D) $\left( - 9 , \frac { 4 } { 3 } \pi \right)$ Select the representation that does not change the location of the given point.

Question 50

Polar Coordinates
1 Plot Points in the Polar Coordinate System
Match the point in polar coordinates with either A, B, C, or D on the graph.
$$\left( - 4 , - \frac { \pi } { 2 } \right)$$

A) $\mathrm { A }$
B) $\mathrm { D }$
C) B
D) $\mathrm { C }$ Use a polar coordinate system to plot the point with the given polar coordinates.

Question 51

Solve the problem.
$( - 1,4 \pi )$

A) $( 1,3 \pi )$
В) $( - 1,5 \pi )$
C) $( - 1,3 \pi )$
D) $( 1,2 \pi )$

Question 52

Convert a Point from Polar to Rectangular Coordinates
$\left( 2 , - 90 ^ { \circ } \right)$

A) $( 0 , - 2 )$
B) $( - 2,0 )$
C) $( 0,2 )$
D) $( 2,0 )$

Question 53

Polar Coordinates
1 Plot Points in the Polar Coordinate System
Match the point in polar coordinates with either A, B, C, or D on the graph.
$\left( 2,315 ^ { \circ } \right)$

A)


B)
C)

D)

Question 54

Use Heron's Formula to Find the Area of a Triangle
$a = 12$ inches, $b = 15$ inches, $c = 4$ inches

A) 14 square inches
B) 27 square inches
C) 12 square inches
D) 29 square inches

Question 55

Polar Coordinates
1 Plot Points in the Polar Coordinate System
Match the point in polar coordinates with either A, B, C, or D on the graph.
$$\left( - 2 , \frac { 5 \pi } { 4 } \right)$$

A)

B)

C)

D)

Question 56

Polar Coordinates
1 Plot Points in the Polar Coordinate System
Match the point in polar coordinates with either A, B, C, or D on the graph.
$( 4,0 )$

A) $\mathrm { C }$
B) $\mathrm { D }$
C) $\mathrm { A }$
D) $B$

Question 57

Polar Coordinates
1 Plot Points in the Polar Coordinate System
Match the point in polar coordinates with either A, B, C, or D on the graph.
$$\left( 4 , \frac { 7 \pi } { 4 } \right)$$

A)

B)

C)

D)

Question 58

Polar Coordinates
1 Plot Points in the Polar Coordinate System
Match the point in polar coordinates with either A, B, C, or D on the graph.
$$\left( - 4 , \frac { - 3 \pi } { 4 } \right)$$

A)

B)

C)

D)

Question 59

Use Heron's Formula to Find the Area of a Triangle
$\mathrm { a } = 11$ meters, $\mathrm { b } = 15$ meters, $c = 6$ meters

A) 28 square meters
B) 14 square meters
C) 56 square meters
D) 58 square meters

Question 60

Solve the problem.
$\left( 8 , \frac { \pi } { 6 } \right) , r > 0$ and $- 2 \pi < \theta < 0$

A) $\left( 8 , - \frac { 11 } { 6 } \pi \right]$
B) $\left( 8 , \frac { 13 } { 6 } \pi \right)$
C) $\left( 8 , - \frac { 5 } { 6 } \pi \right)$
D) $\left( 8 , \frac { 7 } { 6 } \pi \right)$

Question 61

Convert a Point from Rectangular to Polar Coordinates
$( - 2 \sqrt { 2 } , - 2 \sqrt { 2 } )$

A) $\left( 4,225 ^ { \circ } \right)$
B) $\left( 2 \sqrt { 2 } , 225 ^ { \circ } \right)$
C) $\left( 2 \sqrt { 2 } , 135 ^ { \circ } \right)$
D) $\left( 4,135 ^ { \circ } \right)$

Question 62

Convert a Point from Rectangular to Polar Coordinates
$( 0 , - \sqrt { 5 } )$

A) $\left( - \sqrt { 5 } , 90 ^ { \circ } \right)$
B) $\left( - \sqrt { 5 } , 270 ^ { \circ } \right)$
C) $\left( - \sqrt { 5 } , 180 ^ { \circ } \right)$
D) $\left( \sqrt { 5 } , 90 ^ { \circ } \right)$

Question 63

Convert an Equation from Rectangular to Polar Coordinates
$$x = 2$$

A) $r = \frac { 2 } { \cos \theta }$
B) $\mathrm { r } = \frac { 2 } { \sin \theta }$
C) $\cos \theta = 2$
D) $\mathrm { r } = 2$

Question 64

Convert an Equation from Rectangular to Polar Coordinates
$$( x - 12 ) ^ { 2 } + y ^ { 2 } = 144$$

A) $r = 24 \cos \theta$
B) $r = 24 \sin \theta$
C) $r ^ { 2 } = 24 \cos \theta$
D) $r = - 24 \sin \theta + 144$

Question 65

Convert a Point from Rectangular to Polar Coordinates
$( 5 , - 5 )$

A) $\left( - 5 \sqrt { 2 } , 135 ^ { \circ } \right)$
B) $\left( - 5 \sqrt { 2 } , 225 ^ { \circ } \right)$
C) $\left( - 5 \sqrt { 2 } , 45 ^ { \circ } \right)$
D) $\left( 5 \sqrt { 2 } , 135 ^ { \circ } \right)$

Question 66

Convert an Equation from Rectangular to Polar Coordinates
$$\mathrm { y } = 3$$

A) $r = \frac { 3 } { \sin \theta }$
B) $r = \frac { 3 } { \cos \theta }$
C) $\sin \theta = 3$
D) $r = 3$

Question 67

Convert a Point from Rectangular to Polar Coordinates
$( - 12,12 )$

A) $\left( 12 \sqrt { 2 } , \frac { 3 \pi } { 4 } \right)$
B) $\left( 12 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)$
C) $\left( 12 , - \frac { 3 \pi } { 4 } \right)$
D) $\left( 12 , \frac { \pi } { 4 } \right)$

Question 68

Convert an Equation from Rectangular to Polar Coordinates
$2 x - 5 y + 12 = 0$

A) $r = \frac { - 12 } { ( 2 \cos \theta - 5 \sin \theta ) }$
B) $r = \frac { - 12 } { ( 2 \sin \theta - 5 \cos \theta ) }$
C) $2 \cos \theta - 5 \sin \theta = - 12$
D) $2 \cos \theta - 5 \sin \theta = 12$

Question 69

Convert an Equation from Polar to Rectangular Coordinates
$\mathrm { r } \cos \theta = 7$

A) $x = 7$
B) $x ^ { 2 } + y ^ { 2 } = 7$
C) $y ^ { 2 } = 7$
D) $\mathrm { y } = 7$

Question 70

Convert an Equation from Polar to Rectangular Coordinates
$$\theta = \frac { 5 \pi } { 6 }$$

A) $y = - \frac { \sqrt { 3 } } { 3 } x$
B) $y = \sqrt { 3 } x$
C) $y = - \frac { \sqrt { 3 } } { 3 } x ^ { 2 }$
D) $x ^ { 2 } + y ^ { 2 } = 1$

Question 71

Convert a Point from Polar to Rectangular Coordinates
$\left( 5.1 , \frac { \pi } { 9 } \right)$

A) $( 4.8,1.7 )$
В) $( 1.7,4.8 )$
C) $( - 4.8 , - 1.7 )$
D) $( - 1.7 , - 4.8 )$

Question 72

Convert a Point from Rectangular to Polar Coordinates
$( 6 , - 6 \sqrt { 3 } )$

A) $\left( 12 , \frac { 5 \pi } { 3 } \right)$
B) $\left( 6 , \frac { 5 \pi } { 3 } \right)$
C) $\left( 12 , \frac { 11 \pi } { 6 } \right)$
D) $\left( 6 , \frac { 11 \pi } { 6 } \right)$

Question 73

Convert a Point from Polar to Rectangular Coordinates
$\left( - 9 , \frac { 2 \pi } { 3 } \right)$

A) $\left( \frac { 9 } { 2 } , \frac { - 9 \sqrt { 3 } } { 2 } \right)$
B) $\left( - \frac { 9 } { 2 } , \frac { - 9 \sqrt { 3 } } { 2 } \right)$
C) $\left( \frac { 9 } { 2 } , \frac { 9 \sqrt { 3 } } { 2 } \right)$
D) $\left( - \frac { 9 } { 2 } , \frac { 9 \sqrt { 3 } } { 2 } \right)$

Question 74

Convert an Equation from Rectangular to Polar Coordinates
$$y ^ { 2 } = 3 x$$

A) $r = 3 \cot x \csc x$
B) $r = 9 \cot x \csc x$
C) $\mathrm { r } ^ { 2 } ( \cos \theta + \sin \theta ) = 3$
D) $r = 3 \cot ^ { 2 } x$

Question 75

Convert a Point from Polar to Rectangular Coordinates
$\left( 9 , \frac { 3 \pi } { 4 } \right)$

A) $\left( \frac { - 9 \sqrt { 2 } } { 2 } , \frac { 9 \sqrt { 2 } } { 2 } \right)$
B) $\left( \frac { 9 \sqrt { 2 } } { 2 } , \frac { - 9 \sqrt { 2 } } { 2 } \right)$
C) $\left( \frac { 9 \sqrt { 2 } } { 2 } , \frac { 9 \sqrt { 2 } } { 2 } \right)$
D) $\left( \frac { - 9 \sqrt { 2 } } { 2 } , \frac { - 9 \sqrt { 2 } } { 2 } \right)$

Question 76

Convert a Point from Polar to Rectangular Coordinates
$$\left( 5 , - 16 ^ { \circ } \right)$$

A) $( 4.8 , - 1.4 )$
В) $( - 1.4,4.8 )$
C) $( - 4.8,1.4 )$
D) $( 1.4 , - 4.8 )$

Question 77

Convert a Point from Rectangular to Polar Coordinates
$( - 5,0 )$

A) $( 5 , \pi )$
B) $\left( 5 , \frac { \pi } { 2 } \right)$
C) $( 5,0 )$
D) $\left( 5 , \frac { 3 \pi } { 2 } \right)$

Question 78

Convert an Equation from Polar to Rectangular Coordinates
$$\mathrm { r } = 7$$

A) $x ^ { 2 } + y ^ { 2 } = 49$
B) $x = 7$
C) $y ^ { 2 } = 49$
D) $\mathrm { y } = 7$

Question 79

Convert an Equation from Rectangular to Polar Coordinates
$$x ^ { 2 } + y ^ { 2 } = 4$$

A) $\mathrm { r } = 2$
B) $r = 4$
C) $r ( \cos \theta + \sin \theta ) = 2$
D) $r ( \cos \theta + \sin \theta ) = 4$

Question 80

Convert a Point from Rectangular to Polar Coordinates
$( 5 \sqrt { 3 } , 5 )$

A) $\left( 10 , \frac { \pi } { 6 } \right)$
B) $\left( 5 , \frac { \pi } { 6 } \right)$
C) $\left( 10 , \frac { \pi } { 3 } \right)$
D) $\left( 5 , \frac { \pi } { 3 } \right)$