Question 1

Write the complex number in trigonometric form. Answer in radians using both an exact form and an approximate form, rounding to four decimal places.
-4 + 6i

Accepted Answer

The answer of Write the complex number in trigonometric form....

Question 2

Use the following to answer questions :
u =   ; v =  
-Compute u + v.

Accepted Answer

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

Question 3

Use the following to answer questions :
A projectile is launched from a catapult with initial velocity 350 feet/sec at an angle of 65°.
-Find the time(s) required to reach a height of 200 feet? Round to the nearest hundredth.

Accepted Answer

A)  approximately 0.65 sec. 
B)  approximately 20.30 sec. 
C)  approximately 0.65 sec. and 19.17 sec. 
D)  approximately 0.65 sec. and 20.30 sec. 
A)  approximately 0.65 sec. 
B)  approximately 20.30 sec. 
C)  approximately 0.65 sec. and 19.17 sec. 
D)  approximately 0.65 sec. and 20.30 sec.

Question 4

A pilot wishes to fly from Pleasant Hills to Sheldon. She calculates the distances shown using a map, with York for reference since it is due east from Pleasant Hills. What heading should she set for this trip (i.e., what is the measure of angle P)? 91 miles   790 miles

Accepted Answer

A)  3.8° 
B)  4.7° 
C)  5.9° 
D)  6.6° 
A)  3.8° 
B)  4.7° 
C)  5.9° 
D)  6.6°

Question 5

Use the following to answer questions :
A radar ship is 25.0 miles off shore from a major port when a large fleet of ships leaves the port at the 40.0° angle shown.  
-If the maximum range of the ship's radar is 18 miles, approximately how far from port (to the nearest tenth of a mile) is the fleet when it is first detected?

Accepted Answer

A) . $\approx$ 11.0 mi 
B) . $\approx$ 14.6 mi 
C) .$\approx$ 23.9 mi 
D) . $\approx$ 27.3 mi 
A) . $\approx$ 11.0 mi 
B) . $\approx$ 14.6 mi 
C) .$\approx$ 23.9 mi 
D) . $\approx$ 27.3 mi

Question 6

For the vector below, $\theta$represents the acute angle formed by the vector and the x-axis. Write the vector in i, j form. Round to the nearest tenth. v in QIV, |v| = 29, $\theta$= 80°

Accepted Answer

A)  v = 28.6i + 5j 
B)  v = 28.6i - 5j 
C)  v = 5i + 28.6j 
D)  v = 5i - 28.6j 
A)  v = 28.6i + 5j 
B)  v = 28.6i - 5j 
C)  v = 5i + 28.6j 
D)  v = 5i - 28.6j

Question 7

Determine the length to the nearest tenth of a foot of both rafters in the diagram.   42 feet

Accepted Answer

a @#LAT-DLM& 31.8 ft

Question 8

The magnitude of vector v is given, along with the quadrant of the terminal point and the angle it makes with the nearest x-axis. Find the horizontal and vertical components of v and write the results in component form. Round to one decimal place. |v| = 17; $\theta$ = 78°; QIII

Accepted Answer

A)  v =   
B)  v =   
C)  v =   
D)  v =   
A)  v =   
B)  v =   
C)  v =   
D)  v =

Question 9

Use the following to answer questions :
In   $\angle$A = 60°, and side c = 26 ft.
-How many triangles can be formed if side a = 23 ft?

Accepted Answer

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

Question 10

Use the following to answer questions :
In   $\angle$A = 60°, and side c = 26 ft.
-How many triangles can be formed if side a = 17 ft?

Accepted Answer

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

Question 11

Use the following to answer questions :
u = -2i + j; v = 4i + 3j
-Compute u - 5v.

Accepted Answer

A)  -16i - 17j 
B)  -15i - 16j 
C)  -15i - 17j 
D)  -16i - 16j 
A)  -16i - 17j 
B)  -15i - 16j 
C)  -15i - 17j 
D)  -16i - 16j

Question 12

An arrow is shot into the air at an angle of 66° with an initial velocity of 18 ft/sec. Compute the horizontal and vertical components of the representative vector. Round to the nearest tenth.

Accepted Answer

A)  Horizontal component: 7.8 ft/sec; Vertical component: 15.9 ft/sec 
B)  Horizontal component: 15.9 ft/sec; Vertical component: 7.8 ft/sec 
C)  Horizontal component: 16.4 ft/sec; Vertical component: 7.3 ft/sec 
D)  Horizontal component: 7.3 ft/sec; Vertical component: 16.4 ft/sec 
A)  Horizontal component: 7.8 ft/sec; Vertical component: 15.9 ft/sec 
B)  Horizontal component: 15.9 ft/sec; Vertical component: 7.8 ft/sec 
C)  Horizontal component: 16.4 ft/sec; Vertical component: 7.3 ft/sec 
D)  Horizontal component: 7.3 ft/sec; Vertical component: 16.4 ft/sec

Question 13

Graph the complex number using its trigonometric form, then convert it to rectangular form.

Accepted Answer

r = 4, @#IMG-DLM& @#IMG-DLM& (

Question 14

Use the following to answer questions :
u =   ; v =  
-Find the projection of u along v (compute projvu). Round to the nearest hundredth as necessary.

Accepted Answer

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

Question 15

Use the following to answer questions :  
-Compute the quotient   using the trigonometric form. Write your answer in exact rectangular form.

Accepted Answer

A)  4 
B)  -4 
C)  4i 
D)  -4i 
A)  4 
B)  -4 
C)  4i 
D)  -4i

Question 16

Solve for the unknown part.. Round to one decimal place. b2 = (7)2 + (6)2 - 2(7)(6)cos(67°)

Accepted Answer

A)  b = 7.2 
B)  b = 8.0 
C)  b = 8.6 
D)  b = 9.4 
A)  b = 7.2 
B)  b = 8.0 
C)  b = 8.6 
D)  b = 9.4

Question 17

Solve the triangle using the law of sines. If the law of sines cannot be used, state why. Round sides to the nearest tenth.
$\angle$B = 21°
side a = 18 yd
$\angle$C = 84°

Accepted Answer

@#LAT-DLM&A = 75°
b

Question 18

Find the component of u along v (compute compvu) for the vectors u and v given. Round to the nearest hundredth.

Accepted Answer

A)  8.60 tons 
B)  -8.60 tons 
C)  12.29 tons 
D)  -12.29 tons 
A)  8.60 tons 
B)  -8.60 tons 
C)  12.29 tons 
D)  -12.29 tons

Question 19

Assume the law of sines is being applied to solve a triangle. Solve for B (if possible), then determine if a second angle (0° < $\theta$ < 180°) exists that also satisfies the proportion. Round to the nearest tenth of a degree.

Accepted Answer

The answer of Assume the law of sines is being...

Question 20

Use De Moivre's Theorem to compute   .

Accepted Answer

The answer of Use De Moivre's Theorem to compute ...

Write the complex number in trigonometric form. Answer in radians using both an exact form and an approximate form, rounding to four decimal places. -4 + 6i

Use the following to answer questions : u = ; v = -Compute u + v.

Use the following to answer questions : A projectile is launched from a catapult with initial velocity 350 feet/sec at an angle of 65°. -Find the time(s) required to reach a height of 200 feet? Round to the nearest hundredth.

A pilot wishes to fly from Pleasant Hills to Sheldon. She calculates the distances shown using a map, with York for reference since it is due east from Pleasant Hills. What heading should she set for this trip (i.e., what is the measure of angle P)? 91 miles 790 miles

For the vector below, $\theta$ represents the acute angle formed by the vector and the x-axis. Write the vector in i, j form. Round to the nearest tenth. v in QIV, |v| = 29, $\theta$ = 80°

Determine the length to the nearest tenth of a foot of both rafters in the diagram. 42 feet

The magnitude of vector v is given, along with the quadrant of the terminal point and the angle it makes with the nearest x-axis. Find the horizontal and vertical components of v and write the results in component form. Round to one decimal place. |v| = 17; $\theta$ = 78°; QIII

Use the following to answer questions : In $Use the following to answer questions : In \angle A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 23 ft?$ $\angle$ A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 23 ft?

Use the following to answer questions : In $Use the following to answer questions : In \angle A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 17 ft?$ $\angle$ A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 17 ft?

Use the following to answer questions : u = -2i + j; v = 4i + 3j -Compute u - 5v.

An arrow is shot into the air at an angle of 66° with an initial velocity of 18 ft/sec. Compute the horizontal and vertical components of the representative vector. Round to the nearest tenth.

Graph the complex number using its trigonometric form, then convert it to rectangular form.

Use the following to answer questions : u = ; v = -Find the projection of u along v (compute proj_vu). Round to the nearest hundredth as necessary.

Use the following to answer questions : -Compute the quotient using the trigonometric form. Write your answer in exact rectangular form.

Solve for the unknown part.. Round to one decimal place. b² = (7)² + (6)² - 2(7)(6)cos(67°)

Solve the triangle using the law of sines. If the law of sines cannot be used, state why. Round sides to the nearest tenth. $\angle$ B = 21° side a = 18 yd $\angle$ C = 84°

Find the component of u along v (compute comp_vu) for the vectors u and v given. Round to the nearest hundredth.

Use De Moivre's Theorem to compute .

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Exam 7: Applications of Trigonometry

Write the complex number in trigonometric form. Answer in radians using both an exact form and an approximate form, rounding to four decimal places. -4 + 6i

Use the following to answer questions : u = ; v = -Compute u + v.

Use the following to answer questions : A projectile is launched from a catapult with initial velocity 350 feet/sec at an angle of 65°. -Find the time(s) required to reach a height of 200 feet? Round to the nearest hundredth.

A pilot wishes to fly from Pleasant Hills to Sheldon. She calculates the distances shown using a map, with York for reference since it is due east from Pleasant Hills. What heading should she set for this trip (i.e., what is the measure of angle P)? 91 miles 790 miles

For the vector below, θ\thetaθ represents the acute angle formed by the vector and the x-axis. Write the vector in i, j form. Round to the nearest tenth. v in QIV, |v| = 29, θ\thetaθ = 80°

Determine the length to the nearest tenth of a foot of both rafters in the diagram. 42 feet

The magnitude of vector v is given, along with the quadrant of the terminal point and the angle it makes with the nearest x-axis. Find the horizontal and vertical components of v and write the results in component form. Round to one decimal place. |v| = 17; θ\thetaθ = 78°; QIII

Use the following to answer questions : In ∠\angle∠ A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 23 ft?

Use the following to answer questions : In ∠\angle∠ A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 17 ft?

Use the following to answer questions : u = -2i + j; v = 4i + 3j -Compute u - 5v.

An arrow is shot into the air at an angle of 66° with an initial velocity of 18 ft/sec. Compute the horizontal and vertical components of the representative vector. Round to the nearest tenth.

Graph the complex number using its trigonometric form, then convert it to rectangular form.

Use the following to answer questions : u = ; v = -Find the projection of u along v (compute projvu). Round to the nearest hundredth as necessary.

Use the following to answer questions : -Compute the quotient using the trigonometric form. Write your answer in exact rectangular form.

Solve for the unknown part.. Round to one decimal place. b2 = (7)2 + (6)2 - 2(7)(6)cos(67°)

Solve the triangle using the law of sines. If the law of sines cannot be used, state why. Round sides to the nearest tenth. ∠\angle∠ B = 21° side a = 18 yd ∠\angle∠ C = 84°

Find the component of u along v (compute compvu) for the vectors u and v given. Round to the nearest hundredth.

Assume the law of sines is being applied to solve a triangle. Solve for B (if possible), then determine if a second angle (0° < θ\thetaθ < 180°) exists that also satisfies the proportion. Round to the nearest tenth of a degree.

Use De Moivre's Theorem to compute .

Equations and Inequalities

Relations, Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

Systems of Equations and Inequalities

Analytical Geometry

Additional Topics in Algebra

Bridges to Calculus - an Introduction to Limits

Review of Basic Concepts and Skills

Filters

For the vector below, $\theta$ represents the acute angle formed by the vector and the x-axis. Write the vector in i, j form. Round to the nearest tenth. v in QIV, |v| = 29, $\theta$ = 80°

The magnitude of vector v is given, along with the quadrant of the terminal point and the angle it makes with the nearest x-axis. Find the horizontal and vertical components of v and write the results in component form. Round to one decimal place. |v| = 17; $\theta$ = 78°; QIII

Use the following to answer questions : In $Use the following to answer questions : In \angle A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 23 ft?$ $\angle$ A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 23 ft?

Use the following to answer questions : In $Use the following to answer questions : In \angle A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 17 ft?$ $\angle$ A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 17 ft?

Use the following to answer questions : u = ; v = -Find the projection of u along v (compute proj_vu). Round to the nearest hundredth as necessary.

Solve for the unknown part.. Round to one decimal place. b² = (7)² + (6)² - 2(7)(6)cos(67°)

Solve the triangle using the law of sines. If the law of sines cannot be used, state why. Round sides to the nearest tenth. $\angle$ B = 21° side a = 18 yd $\angle$ C = 84°

Find the component of u along v (compute comp_vu) for the vectors u and v given. Round to the nearest hundredth.