Exam 6: Additional Topics in Trigonometry

In the figure below, $a = 9 , b = 11$ , and $c = 12$ . Use this information to solve the parallelogram for $\theta$ . The diagonals of the parallelogram are represented by $c$ and $d$ . Round answer to two decimal places. $In the figure below, a = 9 , b = 11 , and c = 12 . Use this information to solve the parallelogram for \theta . The diagonals of the parallelogram are represented by c and d . Round answer to two decimal places.$

(Multiple Choice)

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Question 41

Find the trigonometric form of the complex number shown below. $- 3 - 3 i$

(Multiple Choice)

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Question 42

Find the component form of vector $\mathbf { v }$ with initial point $( - 5,1 )$ and terminal point $( - 3 , - 2 )$ .

(Multiple Choice)

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Question 43

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. $B = 75 ^ { \circ } 22 ^ { \prime } , a = 11$ , and $c = 14$

(Multiple Choice)

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Question 44

Find the component form of vector $\mathbf { v }$ . $Find the component form of vector \mathbf { v } .$

(Multiple Choice)

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Question 45

Find the angle between the vectors $\mathbf { u }$ and $\mathbf { v }$ . $\mathbf { u } = \cos \left( \frac { \pi } { 3 } \right) \mathbf { i } + \sin \left( \frac { \pi } { 3 } \right) \mathbf { j } , \quad \mathbf { v } = \cos \left( \frac { 5 \pi } { 4 } \right) \mathbf { i } + \sin \left( \frac { 5 \pi } { 4 } \right) \mathbf { j }$

(Multiple Choice)

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Question 46

Plot the following complex number. $3 i$

(Multiple Choice)

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Question 47

Given $\mathbf { u } = \langle - 3,7 \rangle$ and $\mathbf { v } = \langle 1 , - 5 \rangle$ , find $\mathbf { u } \cdot \mathbf { v }$ .

(Multiple Choice)

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Question 48

Given $a = 13 , b = 11$ , and $c = 6$ , use Heron's Area Formula to find the area of triangle $A B C$ . Round answer to two decimal places.

(Multiple Choice)

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Question 49

A plane flies 450 kilometers with a bearing of $319 ^ { \circ }$ from City A to City B (see figure below). The plane then flies 730 kilometers from City B to City C, which is directly west of City A. Find the bearing of the flight from City B to City C. Round your answer to two decimals. $A plane flies 450 kilometers with a bearing of 319 ^ { \circ } from City A to City B (see figure below). The plane then flies 730 kilometers from City B to City C, which is directly west of City A. Find the bearing of the flight from City B to City C. Round your answer to two decimals.$

(Multiple Choice)

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Question 50

Find the vector $\mathbf { v }$ that has a magnitude of 4 and is in the same direction as $\mathbf { u }$ , where $\mathbf { u } = \langle - 5 , - 3 \rangle$ .

(Multiple Choice)

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Question 51

Find the standard form of the complex number shown below. Round answers to two decimal places. $6 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right)$

(Multiple Choice)

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Question 52

Given $a = 7 , b = 5$ , and $c = 8$ , use the Law of Cosines to solve the triangle for the value of $B$ . Round answer to two decimal places.

(Multiple Choice)

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Question 53

Find the trigonometric form of the complex number shown below. $- 3 i$

(Multiple Choice)

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Question 54

A force of 50 pounds is exerted along a rope attached to a crate at an angle of $30 ^ { \circ }$ above the horizontal. The crate is moved 43 feet. How much work has been accomplished? Round answer to one decimal place.

(Multiple Choice)

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Question 55

A 400 -pound trailer is sitting on an exit ramp inclined at $31 ^ { \circ }$ on Highway 35 . How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.

(Multiple Choice)

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Question 56

Find the trigonometric form of the complex number shown below. $- 7 i$

(Multiple Choice)

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Question 57

A force of 45 pounds is exerted along a rope attached to a crate at an angle of $30 ^ { \circ }$ above the horizontal. The crate is moved 50 feet. How much work has been accomplished? Round answer to one decimal place.

(Multiple Choice)

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Question 58

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. $C = 59 ^ { \circ } 24 ^ { \prime } , a = 6$ , and $b = 14.5$

(Multiple Choice)

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Question 59

Given $A = 16 ^ { \circ } , b = 12$ , and $a = 10$ , use the Law of Sines to solve the triangle (if possible) for the value of $c$ . If two solutions exist, find both. Round answer to two decimal places.

(Multiple Choice)

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Question 60

Showing 41 - 60 of 120

Find the trigonometric form of the complex number shown below. $- 3 - 3 i$

Find the component form of vector $\mathbf { v }$ with initial point $( - 5,1 )$ and terminal point $( - 3 , - 2 )$ .

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. $B = 75 ^ { \circ } 22 ^ { \prime } , a = 11$ , and $c = 14$

Find the component form of vector $\mathbf { v }$ . $Find the component form of vector \mathbf { v } .$

Plot the following complex number. $3 i$

Given $\mathbf { u } = \langle - 3,7 \rangle$ and $\mathbf { v } = \langle 1 , - 5 \rangle$ , find $\mathbf { u } \cdot \mathbf { v }$ .

Given $a = 13 , b = 11$ , and $c = 6$ , use Heron's Area Formula to find the area of triangle $A B C$ . Round answer to two decimal places.

Find the vector $\mathbf { v }$ that has a magnitude of 4 and is in the same direction as $\mathbf { u }$ , where $\mathbf { u } = \langle - 5 , - 3 \rangle$ .

Find the standard form of the complex number shown below. Round answers to two decimal places. $6 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right)$

Given $a = 7 , b = 5$ , and $c = 8$ , use the Law of Cosines to solve the triangle for the value of $B$ . Round answer to two decimal places.

Find the trigonometric form of the complex number shown below. $- 3 i$

A force of 50 pounds is exerted along a rope attached to a crate at an angle of $30 ^ { \circ }$ above the horizontal. The crate is moved 43 feet. How much work has been accomplished? Round answer to one decimal place.

A 400 -pound trailer is sitting on an exit ramp inclined at $31 ^ { \circ }$ on Highway 35 . How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.

Find the trigonometric form of the complex number shown below. $- 7 i$

A force of 45 pounds is exerted along a rope attached to a crate at an angle of $30 ^ { \circ }$ above the horizontal. The crate is moved 50 feet. How much work has been accomplished? Round answer to one decimal place.

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. $C = 59 ^ { \circ } 24 ^ { \prime } , a = 6$ , and $b = 14.5$

Given $A = 16 ^ { \circ } , b = 12$ , and $a = 10$ , use the Law of Sines to solve the triangle (if possible) for the value of $c$ . If two solutions exist, find both. Round answer to two decimal places.

Functions and Their Graphs

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Exam 6: Additional Topics in Trigonometry

In the figure below, a=9,b=11a = 9 , b = 11a=9,b=11 , and c=12c = 12c=12 . Use this information to solve the parallelogram for θ\thetaθ . The diagonals of the parallelogram are represented by ccc and ddd . Round answer to two decimal places.

Find the trigonometric form of the complex number shown below. −3−3i- 3 - 3 i−3−3i

Find the component form of vector v\mathbf { v }v with initial point (−5,1)( - 5,1 )(−5,1) and terminal point (−3,−2)( - 3 , - 2 )(−3,−2) .

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. B=75∘22′,a=11B = 75 ^ { \circ } 22 ^ { \prime } , a = 11B=75∘22′,a=11 , and c=14c = 14c=14

Find the component form of vector v\mathbf { v }v .

Plot the following complex number. 3i3 i3i

Given u=⟨−3,7⟩\mathbf { u } = \langle - 3,7 \rangleu=⟨−3,7⟩ and v=⟨1,−5⟩\mathbf { v } = \langle 1 , - 5 \ranglev=⟨1,−5⟩ , find u⋅v\mathbf { u } \cdot \mathbf { v }u⋅v .

Given a=13,b=11a = 13 , b = 11a=13,b=11 , and c=6c = 6c=6 , use Heron's Area Formula to find the area of triangle ABCA B CABC . Round answer to two decimal places.

A plane flies 450 kilometers with a bearing of 319∘319 ^ { \circ }319∘ from City A to City B (see figure below). The plane then flies 730 kilometers from City B to City C, which is directly west of City A. Find the bearing of the flight from City B to City C. Round your answer to two decimals.

Find the vector v\mathbf { v }v that has a magnitude of 4 and is in the same direction as u\mathbf { u }u , where u=⟨−5,−3⟩\mathbf { u } = \langle - 5 , - 3 \rangleu=⟨−5,−3⟩ .

Find the standard form of the complex number shown below. Round answers to two decimal places. 6(cos⁡190∘+isin⁡190∘)6 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right)6(cos190∘+isin190∘)

Given a=7,b=5a = 7 , b = 5a=7,b=5 , and c=8c = 8c=8 , use the Law of Cosines to solve the triangle for the value of BBB . Round answer to two decimal places.

Find the trigonometric form of the complex number shown below. −3i- 3 i−3i

A force of 50 pounds is exerted along a rope attached to a crate at an angle of 30∘30 ^ { \circ }30∘ above the horizontal. The crate is moved 43 feet. How much work has been accomplished? Round answer to one decimal place.

A 400 -pound trailer is sitting on an exit ramp inclined at 31∘31 ^ { \circ }31∘ on Highway 35 . How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.

Find the trigonometric form of the complex number shown below. −7i- 7 i−7i

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30∘30 ^ { \circ }30∘ above the horizontal. The crate is moved 50 feet. How much work has been accomplished? Round answer to one decimal place.

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. C=59∘24′,a=6C = 59 ^ { \circ } 24 ^ { \prime } , a = 6C=59∘24′,a=6 , and b=14.5b = 14.5b=14.5

Given A=16∘,b=12A = 16 ^ { \circ } , b = 12A=16∘,b=12 , and a=10a = 10a=10 , use the Law of Sines to solve the triangle (if possible) for the value of ccc . If two solutions exist, find both. Round answer to two decimal places.

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Find the trigonometric form of the complex number shown below. $- 3 - 3 i$

Find the component form of vector $\mathbf { v }$ with initial point $( - 5,1 )$ and terminal point $( - 3 , - 2 )$ .

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. $B = 75 ^ { \circ } 22 ^ { \prime } , a = 11$ , and $c = 14$

Find the component form of vector $\mathbf { v }$ . $Find the component form of vector \mathbf { v } .$

Plot the following complex number. $3 i$

Given $\mathbf { u } = \langle - 3,7 \rangle$ and $\mathbf { v } = \langle 1 , - 5 \rangle$ , find $\mathbf { u } \cdot \mathbf { v }$ .

Given $a = 13 , b = 11$ , and $c = 6$ , use Heron's Area Formula to find the area of triangle $A B C$ . Round answer to two decimal places.

Find the vector $\mathbf { v }$ that has a magnitude of 4 and is in the same direction as $\mathbf { u }$ , where $\mathbf { u } = \langle - 5 , - 3 \rangle$ .

Find the standard form of the complex number shown below. Round answers to two decimal places. $6 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right)$

Given $a = 7 , b = 5$ , and $c = 8$ , use the Law of Cosines to solve the triangle for the value of $B$ . Round answer to two decimal places.

Find the trigonometric form of the complex number shown below. $- 3 i$

A force of 50 pounds is exerted along a rope attached to a crate at an angle of $30 ^ { \circ }$ above the horizontal. The crate is moved 43 feet. How much work has been accomplished? Round answer to one decimal place.

A 400 -pound trailer is sitting on an exit ramp inclined at $31 ^ { \circ }$ on Highway 35 . How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.

Find the trigonometric form of the complex number shown below. $- 7 i$

A force of 45 pounds is exerted along a rope attached to a crate at an angle of $30 ^ { \circ }$ above the horizontal. The crate is moved 50 feet. How much work has been accomplished? Round answer to one decimal place.

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. $C = 59 ^ { \circ } 24 ^ { \prime } , a = 6$ , and $b = 14.5$

Given $A = 16 ^ { \circ } , b = 12$ , and $a = 10$ , use the Law of Sines to solve the triangle (if possible) for the value of $c$ . If two solutions exist, find both. Round answer to two decimal places.