Question 1

Find the projection of u onto v. ​   ​

Accepted Answer

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

Question 2

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. ​
A = 145°, a = 28, b = 8
​

Accepted Answer

A) B ≈ 0.18°, C ≈ 32.89° 
B) B ≈ 0.18°, C ≈ 39.82° 
C) B ≈ 9.43°, C   25.57° 
D) B ≈ 25.57°, C   9.43° 
E) B ≈ 39.82°, C ≈ 0.18° 
A) B ≈ 0.18°, C ≈ 32.89° 
B) B ≈ 0.18°, C ≈ 39.82° 
C) B ≈ 9.43°, C   25.57° 
D) B ≈ 25.57°, C   9.43° 
E) B ≈ 39.82°, C ≈ 0.18°

Question 3

Find the projection of u onto v. ​   ​

Accepted Answer

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

Question 4

If   and   , and the vectors make angles of 140° and 20° with the x-axis respectively, find the component form of the sum of u and v.Round answers to two decimal places.

Accepted Answer

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

Question 5

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

Accepted Answer

A) -1; scalar 
B)    ; vector 
C)    ; vector 
D) -3; scalar 
E) -5; scalar 
A) -1; scalar 
B)    ; vector 
C)    ; vector 
D) -3; scalar 
E) -5; scalar

Question 6

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​
A = 23°, a = 3, b = 17
​

Accepted Answer

A) Law of Sines; No solution 
B) Law of Cosines; No solution 
C) Law of Cosines; c ≈ 3, B ≈ 43°, C ≈ 114° 
D) Law of Cosines; c ≈ 6, B ≈ 43°, C ≈ 114° 
E) Law of Sines; c ≈ 17, B ≈ 114°, C ≈ 43° 
A) Law of Sines; No solution 
B) Law of Cosines; No solution 
C) Law of Cosines; c ≈ 3, B ≈ 43°, C ≈ 114° 
D) Law of Cosines; c ≈ 6, B ≈ 43°, C ≈ 114° 
E) Law of Sines; c ≈ 17, B ≈ 114°, C ≈ 43°

Question 7

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

Accepted Answer

A) -96; scalar 
B)    ; vector 
C)    ; vector 
D)    ; vector 
E)    ; vector 
A) -96; scalar 
B)    ; vector 
C)    ; vector 
D)    ; vector 
E)    ; vector

Question 8

Find values for b such that the triangle has two solutions. ​
A = 66°, a = 307.6
​

Accepted Answer

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

Question 9

Find the component form of v if   and the angle it makes with the x-axis is 150°.

Accepted Answer

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

Question 10

Find the magnitude and direction angle of   .

Accepted Answer

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

Question 11

Given   and   , determine   .

Accepted Answer

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

Question 12

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129   , b = 9 and c = 7.

Accepted Answer

A) 29.38 sq.units 
B) 24.48 sq.units 
C) 19.58 sq.units 
D) 22.03 sq.units 
E) 26.93 sq.units 
A) 29.38 sq.units 
B) 24.48 sq.units 
C) 19.58 sq.units 
D) 22.03 sq.units 
E) 26.93 sq.units

Question 13

Given   and   , find   .

Accepted Answer

A) 3 
B) -3 
C) -7 
D) 9 
E) -11 
A) 3 
B) -3 
C) -7 
D) 9 
E) -11

Question 14

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

Accepted Answer

A) 0.08 
B) 0.10 
C) 0.12 
D) 0.06 
E) 0.11 
A) 0.08 
B) 0.10 
C) 0.12 
D) 0.06 
E) 0.11

Question 15

Find the area of the triangle having the indicated angle and sides. ​
A = 10°19', b = 4.6, с = 24
​
(Round your answer to one decimal place.)
​

Accepted Answer

A) 9.9 
B) 8.9 
C) 10.9 
D) 11.9 
E) 19.8 
A) 9.9 
B) 8.9 
C) 10.9 
D) 11.9 
E) 19.8

Question 16

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

Accepted Answer

A)    ; vector 
B)    ; vector 
C)    ; vector 
D) -240; scalar 
E)    ; vector 
A)    ; vector 
B)    ; vector 
C)    ; vector 
D) -240; scalar 
E)    ; vector

Question 17

Find the angle between the vectors u and v if   and   Round your answer to two decimal places.

Accepted Answer

A) 66.14° 
B) 68.34° 
C) 67.38° 
D) 65.45° 
E) 68.79° 
A) 66.14° 
B) 68.34° 
C) 67.38° 
D) 65.45° 
E) 68.79°

Question 18

Find 2u - 3v. ​   ​

Accepted Answer

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

Question 19

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point
Terminal Point
(-9, 9)​
​(10, -10)

Accepted Answer

A) 19i - 19j 
B) ​-19i + 19j 
C) ​​-19i - 19j 
D) ​19i + 19j 
E) ​-19i - 19j 
A) 19i - 19j 
B) ​-19i + 19j 
C) ​​-19i - 19j 
D) ​19i + 19j 
E) ​-19i - 19j

Question 20

Use the Heron's formula to find the area of the triangle.Round your answer to two decimal places. ​
A = 10, b = 14, c = 19
​

Accepted Answer

A) 14.68 
B) 84.31 
C) 54.99 
D) 31.75 
E) 68.09 
A) 14.68 
B) 84.31 
C) 54.99 
D) 31.75 
E) 68.09

Find the projection of u onto v.

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. A = 145°, a = 28, b = 8

Find the projection of u onto v.

If and , and the vectors make angles of 140° and 20° with the x-axis respectively, find the component form of the sum of u and v.Round answers to two decimal places.

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

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. A = 23°, a = 3, b = 17

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

Find values for b such that the triangle has two solutions. A = 66°, a = 307.6

Find the component form of v if and the angle it makes with the x-axis is 150°.

Find the magnitude and direction angle of .

Given and , determine .

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129 , b = 9 and c = 7.

Given and , find .

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

Find the area of the triangle having the indicated angle and sides. A = 10°19', b = 4.6, с = 24 (Round your answer to one decimal place.)

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

Find the angle between the vectors u and v if and Round your answer to two decimal places.

Find 2u - 3v.

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9, 9) (10, -10)

Use the Heron's formula to find the area of the triangle.Round your answer to two decimal places. A = 10, b = 14, c = 19

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 3: Additional-Topics-In-Trigonometry

Find the projection of u onto v. ​ ​

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. ​ A = 145°, a = 28, b = 8 ​

Find the projection of u onto v. ​ ​

If and , and the vectors make angles of 140° and 20° with the x-axis respectively, find the component form of the sum of u and v.Round answers to two decimal places.

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

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​ A = 23°, a = 3, b = 17 ​

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

Find values for b such that the triangle has two solutions. ​ A = 66°, a = 307.6 ​

Find the component form of v if and the angle it makes with the x-axis is 150°.

Find the magnitude and direction angle of .

Given and , determine .

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129 , b = 9 and c = 7.

Given and , find .

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

Find the area of the triangle having the indicated angle and sides. ​ A = 10°19', b = 4.6, с = 24 ​ (Round your answer to one decimal place.) ​

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

Find the angle between the vectors u and v if and Round your answer to two decimal places.

Find 2u - 3v. ​ ​

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9, 9)​ ​(10, -10)

Use the Heron's formula to find the area of the triangle.Round your answer to two decimal places. ​ A = 10, b = 14, c = 19 ​

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Find the projection of u onto v.

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. A = 145°, a = 28, b = 8

Find the projection of u onto v.

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

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. A = 23°, a = 3, b = 17

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

Find values for b such that the triangle has two solutions. A = 66°, a = 307.6

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

Find the area of the triangle having the indicated angle and sides. A = 10°19', b = 4.6, с = 24 (Round your answer to one decimal place.)

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

Find 2u - 3v.

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9, 9) (10, -10)

Use the Heron's formula to find the area of the triangle.Round your answer to two decimal places. A = 10, b = 14, c = 19