Question 1

Find the absolute value of the complex number.
-9 + 2i

Accepted Answer

A)  11 
B)    
C)  85 
D)    
A)  11 
B)    
C)  85 
D)

Question 2

For the point given in rectangular coordinates, find equivalent polar coordinates  
-(

Accepted Answer

A)  (2, 300°) 
B)  (4, 160°) 
C)  (4, 120°) 
D)  (8, 120°) 
A)  (2, 300°) 
B)  (4, 160°) 
C)  (4, 120°) 
D)  (8, 120°)

Question 3

Find the component form for the vector with the given magnitude and direction angle   . Round values to the nearest
tenth.
-

Accepted Answer

A)  38, -89.0 
B)  38, 89 
C)  -89.0, 38 
D)  89, 38 
A)  38, -89.0 
B)  38, 89 
C)  -89.0, 38 
D)  89, 38

Question 4

Graph the pair of polar equations on a calculator, together on the same screen, and use the trace feature to estimate the
polar coordinates of all points of intersection of the curves. Round to the nearest hundredth, if necessary.
-

Accepted Answer

A)  (0, 0), (5, 0), (5, 3.14) 
B)  (0, 5), (3.14, 5) 
C)  (5, 0), (5, 3.14) 
D)  (0, 0), (0, 5), (3.14, 5) 
A)  (0, 0), (5, 0), (5, 3.14) 
B)  (0, 5), (3.14, 5) 
C)  (5, 0), (5, 3.14) 
D)  (0, 0), (0, 5), (3.14, 5)

Question 5

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
-0, -2

Accepted Answer

A)  2; 90° 
B)  2; 180° 
C)  4; 270° 
D)  2; 270° 
A)  2; 90° 
B)  2; 180° 
C)  4; 270° 
D)  2; 270°

Question 6

Solve the problem.
-A force of 659 lb is required to pull a boat up a ramp inclined at 15.0° with the horizontal. How much does the boat weigh? Round to the nearest pound.

Accepted Answer

A)  644 lb 
B)  2550 lb 
C)  3190 lb 
D)  637 lb 
A)  644 lb 
B)  2550 lb 
C)  3190 lb 
D)  637 lb

Question 7

Perform the operation on the given vectors and find the magnitude and direction angle for the new vector.
-Given A = 5, 2 and B = 3, 5 A - B

Accepted Answer

A)    
B)    
C)    
D)  6, 56.3° 
A)    
B)    
C)    
D)  6, 56.3°

Question 8

Provide an appropriate response.
-What happens if C = 90° when the law of cosines is applied in the form

Accepted Answer

The answer of Provide an appropriate response.
-What happens if C...

Question 9

Perform the indicated operation. Use the form for vectors. -v = <6, 7>; Find 6v.

Accepted Answer

A) <12, 7> B) <36, 42> C) <36, 7> D) <12, 13> A) <12, 7> B) <36, 42> C) <36, 7> D) <12, 13>

Question 10

Solve the equation. Write the answer in a + bi form.
-  - i = 0

Accepted Answer

A)  -1, 1 
B)  -i, i 
C)    
D)    
A)  -1, 1 
B)  -i, i 
C)    
D)

Question 11

Solve the problem.
-A projectile is fired from a height of 8.7 feet with an initial velocity of 151 ft/sec at an angle of 30° with the horizontal. The parametric equations for the path of the projectile are   where x and y are in feet and t is in seconds. Find the total horizontal distance traveled by the projectile. Round
Your answer to the nearest tenth of a foot.

Accepted Answer

A)  933.8 feet 
B)  617.1 feet 
C)  631.7 feet 
D)  466.9 feet 
A)  933.8 feet 
B)  617.1 feet 
C)  631.7 feet 
D)  466.9 feet

Question 12

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
-2, 2

Accepted Answer

A)  4; 45° 
B)  2; 225° 
C)    
D)    
A)  4; 45° 
B)  2; 225° 
C)    
D)

Question 13

Graph the pair of parametric equations in the rectangular coordinate system.
-

Accepted Answer

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

Question 14

Provide an appropriate response.
-In your own words, explain what De Moivre's Theorem is used for and how to apply it.

Accepted Answer

De Moivre's Theorem is a mathematical fo

Question 15

Find the magnitude of the horizontal and the vertical components for the vector with the given magnitude and direction
angle   Round to the nearest tenth.
-

Accepted Answer

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

Question 16

Change the polar coordinates   to rectangular coordinates (x, y).
-

Accepted Answer

A)  (0, -1) 
B)  (0, 1) 
C)  (-1, 0) 
D)  (1, 0) 
A)  (0, -1) 
B)  (0, 1) 
C)  (-1, 0) 
D)  (1, 0)

Question 17

Express the given vector as a linear combination of the unit vectors i and j.
-

Accepted Answer

A)    
B)    
C)  2i + 16j 
D)    
A)    
B)    
C)  2i + 16j 
D)

Question 18

Determine the number of triangles with the given parts.
-a = 4, b = 8, c = 11

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  3 
A)  0 
B)  1 
C)  2 
D)  3

Question 19

Identify the graph of the pair of parametric equations.
-x = -8t + 6, y = -4 - 4t

Accepted Answer

A)  Parabola 
B)  Line 
C)  Circle 
D)  Ellipse 
A)  Parabola 
B)  Line 
C)  Circle 
D)  Ellipse

Question 20

Approximate the area of the triangle to the nearest tenth.
-

Accepted Answer

A)  1380.1 
B)  1401.2 
C)  1388.4 
D)  1371.6 
A)  1380.1 
B)  1401.2 
C)  1388.4 
D)  1371.6

Find the absolute value of the complex number. -9 + 2i

For the point given in rectangular coordinates, find equivalent polar coordinates -(

Find the component form for the vector with the given magnitude and direction angle . Round values to the nearest tenth. -

Graph the pair of polar equations on a calculator, together on the same screen, and use the trace feature to estimate the polar coordinates of all points of intersection of the curves. Round to the nearest hundredth, if necessary. -

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. -0, -2

Solve the problem. -A force of 659 lb is required to pull a boat up a ramp inclined at 15.0° with the horizontal. How much does the boat weigh? Round to the nearest pound.

Perform the operation on the given vectors and find the magnitude and direction angle for the new vector. -Given A = 5, 2 and B = 3, 5 A - B

Provide an appropriate response. -What happens if C = 90° when the law of cosines is applied in the form

Perform the indicated operation. Use the form <a, b> for vectors. -v = <6, 7>; Find 6v.

Solve the equation. Write the answer in a + bi form. - - i = 0

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. -2, 2

Graph the pair of parametric equations in the rectangular coordinate system. -

Provide an appropriate response. -In your own words, explain what De Moivre's Theorem is used for and how to apply it.

Find the magnitude of the horizontal and the vertical components for the vector with the given magnitude and direction angle Round to the nearest tenth. -

Change the polar coordinates to rectangular coordinates (x, y). -

Express the given vector as a linear combination of the unit vectors i and j. -

Determine the number of triangles with the given parts. -a = 4, b = 8, c = 11

Identify the graph of the pair of parametric equations. -x = -8t + 6, y = -4 - 4t

Approximate the area of the triangle to the nearest tenth. -

Equations, Inequalities, and Modeling

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The Trigonometric Functions

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Exam 7: Applications of Trigonometry