Question 1

​Find a unit vector in the direction of   . ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 2

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​
A = 35°, B = 60°, c = 10
​

Accepted Answer

A) C = 85°, a ​≈ 6.76, b ≈ 8.69 
B) C = 85°, a ​≈ 8.69, b ≈ 9.69 
C) C = 85°, a ​≈ 8.76, b ≈ 10.69 
D) C = 85°, a ​≈ 5.76, b ≈ 8.69 
E) ​C = 85°, a ​≈ 7.76, b ≈ 10.69 
A) C = 85°, a ​≈ 6.76, b ≈ 8.69 
B) C = 85°, a ​≈ 8.69, b ≈ 9.69 
C) C = 85°, a ​≈ 8.76, b ≈ 10.69 
D) C = 85°, a ​≈ 5.76, b ≈ 8.69 
E) ​C = 85°, a ​≈ 7.76, b ≈ 10.69

Question 3

Use the vectors   ,   to find the indicated quantity.State whether the result is a vector or a scalar. ​   ​

Accepted Answer

A)    ; vector 
B)    ; vector 
C) -72; scalar 
D) 60; scalar 
E)    ; vector 
A)    ; vector 
B)    ; vector 
C) -72; scalar 
D) 60; scalar 
E)    ; vector

Question 4

Find a unit vector in the direction of the given vector. ​   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E)    
A) ​   
B) ​   
C) ​   
D) ​   
E)

Question 5

Find values for b such that the triangle has one solution. ​
A = 24​°, a = 16.2
​

Accepted Answer

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

Question 6

Given a = 10, b = 12, and c = 8, use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places. ​

Accepted Answer

A) 82.82° 
B) 55.77° 
C) 41.41° 
D) 80.44° 
E) 60.33° 
A) 82.82° 
B) 55.77° 
C) 41.41° 
D) 80.44° 
E) 60.33°

Question 7

Use the vector   to find the indicated quantity.State whether the result is a vector or a scalar. ​   ​

Accepted Answer

A)    ; vector 
B) 15; scalar 
C) 13; scalar 
D) 11; scalar 
E)    ; vector 
A)    ; vector 
B) 15; scalar 
C) 13; scalar 
D) 11; scalar 
E)    ; vector

Question 8

Find u + v. ​   ​

Accepted Answer

A) ​   
B)    ​ 
C) ​   
D) ​   
E) ​   
A) ​   
B)    ​ 
C) ​   
D) ​   
E) ​

Question 9

Use vectors to find the measure of the angle at vertex B of triangle ABC, when   ,   , and   .Round answer to two decimal places.

Accepted Answer

A) 95.94° 
B) 98.47° 
C) 97.13° 
D) 95.04° 
E) 99.65° 
A) 95.94° 
B) 98.47° 
C) 97.13° 
D) 95.04° 
E) 99.65°

Question 10

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​   a = 9, b = 5, c = 10

Accepted Answer

A) A ≈ 29.93°, B ≈ 63.90°, C ≈ 86.18° 
B) A ≈ 86.18°, B ≈ 29.93°, C ≈ 63.90° 
C) A ≈ 86.18°, B ≈ 63.90°, C ≈ 29.93° 
D) A ≈ 63.90°, B ≈ 86.18°, C ≈ 29.93° 
E) A ≈ 63.90°, B ≈ 29.93°, C ≈ 86.18° 
A) A ≈ 29.93°, B ≈ 63.90°, C ≈ 86.18° 
B) A ≈ 86.18°, B ≈ 29.93°, C ≈ 63.90° 
C) A ≈ 86.18°, B ≈ 63.90°, C ≈ 29.93° 
D) A ≈ 63.90°, B ≈ 86.18°, C ≈ 29.93° 
E) A ≈ 63.90°, B ≈ 29.93°, C ≈ 86.18°

Question 11

Find the angle θ between the vectors. ​
​   ​
(Round the answer to 2 decimal places.)
​

Accepted Answer

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

Question 12

Find values for b such that the triangle has two solutions. ​
A = 46°, a = 10
​

Accepted Answer

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

Question 13

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 75.4, b = 52, c = 52
​
​

Accepted Answer

A) A ≈ 43.53°, B ≈ 92.94°, C ≈ 43.53° 
B) A ≈ 43.53°, B ≈ 97.94°, C ≈ 38.53° 
C) A ≈ 43.53°, B ≈ 38.53°, C ≈ 97.94° 
D) A ≈ 92.94°, B ≈ 43.53°, C ≈ 43.53° 
E) A ≈ 97.94°, B ≈ 38.53°, C ≈ 43.53° 
A) A ≈ 43.53°, B ≈ 92.94°, C ≈ 43.53° 
B) A ≈ 43.53°, B ≈ 97.94°, C ≈ 38.53° 
C) A ≈ 43.53°, B ≈ 38.53°, C ≈ 97.94° 
D) A ≈ 92.94°, B ≈ 43.53°, C ≈ 43.53° 
E) A ≈ 97.94°, B ≈ 38.53°, C ≈ 43.53°

Question 14

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. ​
A = 120°, a = b = 36
​

Accepted Answer

A) B ≈ 108°, C ≈ 36°, c ≈ 44 
B) B ≈ 36°, C ≈ 108°, c ≈ 23.5 
C) B ≈ 105°, C ≈ 39°, c ≈ 23.5 
D) B ≈ 29°, C ≈ 115°, c ≈ 23.5 
E) No Solution 
A) B ≈ 108°, C ≈ 36°, c ≈ 44 
B) B ≈ 36°, C ≈ 108°, c ≈ 23.5 
C) B ≈ 105°, C ≈ 39°, c ≈ 23.5 
D) B ≈ 29°, C ≈ 115°, c ≈ 23.5 
E) No Solution

Question 15

Given vectors   ,   and   determine whether the result of the following expression is a vector or a scalar.   ​

Accepted Answer

A) vector 
B) scalar 
A) vector 
B) scalar

Question 16

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​
A = 78.2, b = 52, c = 52
​

Accepted Answer

A) 771.91 
B) ​140.43 
C) ​80.66 
D) ​769.91 
E) 1340.39 
A) 771.91 
B) ​140.43 
C) ​80.66 
D) ​769.91 
E) 1340.39

Question 17

To determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle between them (see figure).Determine the distance a between the planes when A = 52° miles, b = 22 miles, and c = 19 miles. ​   ​

Accepted Answer

A) 18.2 mi 
B) 20.2 mi 
C) 36.9 mi 
D) 24.2 mi 
E) 21.2 mi 
A) 18.2 mi 
B) 20.2 mi 
C) 36.9 mi 
D) 24.2 mi 
E) 21.2 mi

Question 18

Find the component form of v if   and the angle it makes with the x-axis is 60°.

Accepted Answer

A) ​   
B) ​   
C)    
D) ​   
E) ​   
A) ​   
B) ​   
C)    
D) ​   
E) ​

Question 19

Find the angle θ between the vectors. ​   ​
(Round the answer to 2 decimal places.)
​

Accepted Answer

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

Question 20

​Find the magnitude of vector v with initial point (7, 5) and terminal point (-3, -5). ​

Accepted Answer

A) ​   
B) ​14 
C) ​   
D) ​   
E) ​   
A) ​   
B) ​14 
C) ​   
D) ​   
E) ​

Find a unit vector in the direction of .

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. A = 35°, B = 60°, c = 10

Use the vectors , to find the indicated quantity.State whether the result is a vector or a scalar.

Find a unit vector in the direction of the given vector.

Find values for b such that the triangle has one solution. A = 24°, a = 16.2

Given a = 10, b = 12, and c = 8, use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places.

Use the vector to find the indicated quantity.State whether the result is a vector or a scalar.

Find u + v.

Use vectors to find the measure of the angle at vertex B of triangle ABC, when , , and .Round answer to two decimal places.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. a = 9, b = 5, c = 10

Find the angle θ between the vectors. (Round the answer to 2 decimal places.)

Find values for b such that the triangle has two solutions. A = 46°, a = 10

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. A = 75.4, b = 52, c = 52

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. A = 120°, a = b = 36

Given vectors , and determine whether the result of the following expression is a vector or a scalar.

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 78.2, b = 52, c = 52

To determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle between them (see figure).Determine the distance a between the planes when A = 52° miles, b = 22 miles, and c = 19 miles.

Find the component form of v if and the angle it makes with the x-axis is 60°.

Find the angle θ between the vectors. (Round the answer to 2 decimal places.)

Find the magnitude of vector v with initial point (7, 5) and terminal point (-3, -5).

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 3: Additional-Topics-In-Trigonometry

​Find a unit vector in the direction of . ​

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​ A = 35°, B = 60°, c = 10 ​

Use the vectors , to find the indicated quantity.State whether the result is a vector or a scalar. ​ ​

Find a unit vector in the direction of the given vector. ​ ​

Find values for b such that the triangle has one solution. ​ A = 24​°, a = 16.2 ​

Given a = 10, b = 12, and c = 8, use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places. ​

Use the vector to find the indicated quantity.State whether the result is a vector or a scalar. ​ ​

Find u + v. ​ ​

Use vectors to find the measure of the angle at vertex B of triangle ABC, when , , and .Round answer to two decimal places.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ a = 9, b = 5, c = 10

Find the angle θ between the vectors. ​ ​ ​ (Round the answer to 2 decimal places.) ​

Find values for b such that the triangle has two solutions. ​ A = 46°, a = 10 ​

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 75.4, b = 52, c = 52 ​ ​

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. ​ A = 120°, a = b = 36 ​

Given vectors , and determine whether the result of the following expression is a vector or a scalar. ​

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​ A = 78.2, b = 52, c = 52 ​

To determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle between them (see figure).Determine the distance a between the planes when A = 52° miles, b = 22 miles, and c = 19 miles. ​ ​

Find the component form of v if and the angle it makes with the x-axis is 60°.

Find the angle θ between the vectors. ​ ​ (Round the answer to 2 decimal places.) ​

​Find the magnitude of vector v with initial point (7, 5) and terminal point (-3, -5). ​

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Find a unit vector in the direction of .

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. A = 35°, B = 60°, c = 10

Use the vectors , to find the indicated quantity.State whether the result is a vector or a scalar.

Find a unit vector in the direction of the given vector.

Find values for b such that the triangle has one solution. A = 24°, a = 16.2

Given a = 10, b = 12, and c = 8, use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places.

Use the vector to find the indicated quantity.State whether the result is a vector or a scalar.

Find u + v.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. a = 9, b = 5, c = 10

Find the angle θ between the vectors. (Round the answer to 2 decimal places.)

Find values for b such that the triangle has two solutions. A = 46°, a = 10

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. A = 75.4, b = 52, c = 52

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. A = 120°, a = b = 36

Given vectors , and determine whether the result of the following expression is a vector or a scalar.

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 78.2, b = 52, c = 52

To determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle between them (see figure).Determine the distance a between the planes when A = 52° miles, b = 22 miles, and c = 19 miles.

Find the angle θ between the vectors. (Round the answer to 2 decimal places.)

Find the magnitude of vector v with initial point (7, 5) and terminal point (-3, -5).