Question 1

Find u + v. 
 $\mathbf { u } = \langle 6,1 \rangle , \mathbf { v } = \langle 1,7 \rangle$

Accepted Answer

A)   $\langle 8,9 \rangle$ 
B)  $\langle 7,8 \rangle$ 
C)   $\langle 8,8 \rangle$ 
D)   $\langle 8,7 \rangle$ 
E)   $\langle 7,7 \rangle$

Question 2

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form. $- 7 ( \sqrt { 3 } + i ) ^ { 5 }$

Accepted Answer

A)  $112 \sqrt { 3 } - 112 i$ 
B)  $7 \sqrt { 3 } + 7 i$ 
C)  $- 112 \sqrt { 3 } + 112 i$ 
D)  $7 + 7 \sqrt { 3 } i$ 
E)   $112 \sqrt { 3 } + 112 i$

Question 3

Use DeMoivre's Theorem to find the indicated power of the following complex number. $( - 3 + 3 i ) ^ { 4 }$

Accepted Answer

A) -5,184 
B) 46,656 
C) 5,184 
D) 186,624 
E) 7,776

Question 4

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

Accepted Answer

A)   $10 \sqrt { 2 }$ 
B)  14 
C)   $20 \sqrt { 2 }$ 
D)   $\sqrt { 74 }$ 
E)   $2 \sqrt { 51 }$

Question 5

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place.
​

Accepted Answer

A) 1,812.8 lb 
B) 1,810.8 lb 
C) 1,814.8 lb 
D) 1,811.8 lb 
E) 1,813.8 lb

Question 6

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

Accepted Answer

A)  $307.6  b > \frac { 307.6 } { \sin 66 ^ { \circ } }$ 
D)  $307.6 < b < \frac { 307.6 } { \sin 66 ^ { \circ } }$ 
E)  $307.6 \leq b \leq \frac { 307.6 } { \sin 66 ^ { \circ } }$

Question 7

A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ1 = 40° and θ2 = 35°.Approximate the answers to one decimal place. ​  ​

Accepted Answer

A) ​​TL = 12.7 lb; TR = 12.7 lb 
B) ​TL = 11.9 lb; TR = 11.9 lb 
C) ​TL = 11.9 lb; TR = 12.7 lb 
D) TL = 12.7 lb; TR = 11.9 lb 
E) ​​TL = 13.7 lb; TR = 12.9 lb

Question 8

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.) ​

Accepted Answer

A) Vertical ≈ -55.7 mi/h, Horizontal ≈ 91.7 mi/h. 
B) Vertical ≈ 90.7 mi/h, Horizontal ≈ -56.7 mi/h. 
C) Vertical ≈ -56.7 mi/h, Horizontal ≈ -56.7 mi/h. 
D) Vertical ≈ -56.7 mi/h, Horizontal ≈ 90.7 mi/h. 
E) Vertical ≈ 90.7 mi/h, Horizontal ≈ 90.7 mi/h.

Question 9

Find the trigonometric form of $- 14 \sqrt { 3 } + 14 i$ .

Accepted Answer

A)   $14 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right)$ 
B)   $196 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
C)   $14 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
D)   $28 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
E)   $28 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right)$

Question 10

Find the standard form of the complex number $10 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$ .Round values to the nearest hundredth.

Accepted Answer

A) 9.66 - 2.59i 
B)  8.66 + 5i 
C)  -9.66 - 2.59i 
D)  -8.66 - 5i 
E)  9.66 + 2.59i

Question 11

Find values for b such that the triangle has two solutions.  
A = 10°, a = 18.6

Accepted Answer

A)  $18.6  b > \frac { 18.6 } { \sin 10 ^ { \circ } }$ 
D)  $18.6 \leq b \leq \frac { 18.6 } { \sin 10 ^ { \circ } }$ 
E)  $18.6 \geq b \geq \frac { 18.6 } { \sin 10 ^ { \circ } }$

Question 12

A loaded barge is being towed by two tugboats, and the magnitude of the resultant is 6,400 pounds directed along the axis of the barge (see figure).Find the tension in the tow lines if they each make an angle 21° with the axis of the barge.Approximate the answer to one decimal place. ​  ​
Where a = 21°.

Accepted Answer

A) 3,425.7 lb 
B) 3,429.7 lb 
C) 3,426.7 lb 
D) 3,428.7 lb 
E) 3,427.7 lb

Question 13

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.  $9 \left( \cos 62 ^ { \circ } + i \sin 62 ^ { \circ } \right)$

Accepted Answer

A) 7.9465 + 4.2252i 
B) 4.2252 + 7.9465i 
C) 4.2252 - 7.9465i 
D) 7.9465 - 4.2252i 
E) None of the above

Question 14

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.   $14 \left( \cos \frac { 2 \pi } { 5 } + i \sin \frac { 2 \pi } { 5 } \right)$

Accepted Answer

A) 4.3262 + 13.3148i 
B) 13.3148 + 4.3262i 
C) 13.3148 - 4.3262i 
D) 4.3262 - 13.3148i 
E) None of the above

Question 15

Plot the complex number and find its absolute value.  
-4i

Accepted Answer

A)      $| - 4 i | = - 5$ 
B)      $| - 4 i | = 6$ 
C)      $| - 4 i | = - 6$ 
D)     $| - 4 i | = 5$ 
E)      $| - 4 i | = 4$

Question 16

Find the dot product of u and v. 
 $\begin{array} { l } 
\mathbf { u } = \langle - 7,1 \rangle \
\mathbf { v } = \langle 4 , - 5 \rangle
\end{array}$

Accepted Answer

A) -31 
B) -29 
C) -33 
D) -37 
E) -35

Question 17

Find values for b such that the triangle has no solutions.  
A = 24°, a = 13

Accepted Answer

A)   $b \leq \frac { 13 } { \sin 24 ^ { \circ } }$ 
B)  $b > \frac { 13 } { \sin 24 ^ { \circ } }$ 
C)  $b = \frac { 13 } { \sin 24 ^ { \circ } }$ 
D)  $b < \frac { 13 } { \sin 24 ^ { \circ } }$ 
E)  $b \geq \frac { 13 } { \sin 24 ^ { \circ } }$

Question 18

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

Accepted Answer

A)   $5 \sqrt { 2 } \left( \cos \left( \arctan \left( \frac { 2 } { 21 } \right) \right) + i \sin \left( \arctan \left( \frac { 2 } { 21 } \right) \right) \right)$ 
B)   $5 \sqrt { 2 } \left( \cos \left( \arctan \left( - \frac { 3 } { 7 } \right) \right) + i \sin \left( \arctan \left( - \frac { 3 } { 7 } \right) \right) \right)$ 
C)   $5 \sqrt { 2 } \left( \cos \left( \arctan \left( - \frac { 3 } { 35 } \right) \right) + i \sin \left( \arctan \left( - \frac { 3 } { 35 } \right) \right) \right)$ 
D)   $5 \sqrt { 2 } \left( \cos \left( \arctan \left( \frac { 1 } { 7 } \right) \right) + i \sin \left( \arctan \left( \frac { 1 } { 7 } \right) \right) \right)$ 
E)  $5 \sqrt { 2 } \left( \cos \left( \arctan \left( \frac { 1 } { 14 } \right) \right) + i \sin \left( \arctan \left( \frac { 1 } { 14 } \right) \right) \right)$

Question 19

Determine the work done by a person lifting a 240-newton bag of sugar 2 meters.

Accepted Answer

A) 510 N-m 
B) 480 N-m 
C) 520 N-m 
D) 500 N-m 
E) 490 N-m

Question 20

Find the area of the triangle having the indicated angle and sides. ​
B = 71°20', a = 62, c = 24
​
(Round your answer to one decimal place.)
​

Accepted Answer

A) 705.9 
B) ​703.9 
C) ​706.9 
D) ​704.9 
E) ​1,409.7

Exam 6: Additional Topics In Trigonometery

Find u + v. $\mathbf { u } = \langle 6,1 \rangle , \mathbf { v } = \langle 1,7 \rangle$

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form. $- 7 ( \sqrt { 3 } + i ) ^ { 5 }$

Use DeMoivre's Theorem to find the indicated power of the following complex number. $( - 3 + 3 i ) ^ { 4 }$

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

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place.

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

A traffic light weighing 15 pounds is suspended by two cables (see figure) .Find the tension in each cable if θ₁ = 40° and θ₂ = 35°.Approximate the answers to one decimal place.

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.)

Find the trigonometric form of $- 14 \sqrt { 3 } + 14 i$ .

Find the standard form of the complex number $10 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$ .Round values to the nearest hundredth.

Find values for b such that the triangle has two solutions. A = 10°, a = 18.6

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $9 \left( \cos 62 ^ { \circ } + i \sin 62 ^ { \circ } \right)$

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $14 \left( \cos \frac { 2 \pi } { 5 } + i \sin \frac { 2 \pi } { 5 } \right)$

Plot the complex number and find its absolute value. -4i

Find the dot product of u and v. $\begin{array} { l } \mathbf { u } = \langle - 7,1 \rangle \\\mathbf { v } = \langle 4 , - 5 \rangle\end{array}$

Find values for b such that the triangle has no solutions. A = 24°, a = 13

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

Determine the work done by a person lifting a 240-newton bag of sugar 2 meters.

Find the area of the triangle having the indicated angle and sides. B = 71°20', a = 62, c = 24 (Round your answer to one decimal place.)

Exam 6: Additional Topics In Trigonometery

Find u + v. u=⟨6,1⟩,v=⟨1,7⟩\mathbf { u } = \langle 6,1 \rangle , \mathbf { v } = \langle 1,7 \rangleu=⟨6,1⟩,v=⟨1,7⟩

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form. −7(3+i) 5- 7 ( \sqrt { 3 } + i ) ^ { 5 }−7(3​+i) 5

Use DeMoivre's Theorem to find the indicated power of the following complex number. (−3+3i) 4( - 3 + 3 i ) ^ { 4 }(−3+3i) 4

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

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place. ​

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

A traffic light weighing 15 pounds is suspended by two cables (see figure) .Find the tension in each cable if θ1 = 40° and θ2 = 35°.Approximate the answers to one decimal place. ​ ​

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.) ​

Find the trigonometric form of −143+14i- 14 \sqrt { 3 } + 14 i−143​+14i .

Find the standard form of the complex number 10(cos⁡π12+isin⁡π12) 10 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right) 10(cos12π​+isin12π​) .Round values to the nearest hundredth.

Find values for b such that the triangle has two solutions. A = 10°, a = 18.6

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. 9(cos⁡62∘+isin⁡62∘) 9 \left( \cos 62 ^ { \circ } + i \sin 62 ^ { \circ } \right) 9(cos62∘+isin62∘)

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. 14(cos⁡2π5+isin⁡2π5) 14 \left( \cos \frac { 2 \pi } { 5 } + i \sin \frac { 2 \pi } { 5 } \right) 14(cos52π​+isin52π​)

Plot the complex number and find its absolute value. -4i

Find the dot product of u and v. u=⟨−7,1⟩v=⟨4,−5⟩\begin{array} { l } \mathbf { u } = \langle - 7,1 \rangle \\\mathbf { v } = \langle 4 , - 5 \rangle\end{array}u=⟨−7,1⟩v=⟨4,−5⟩​

Find values for b such that the triangle has no solutions. A = 24°, a = 13

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

Determine the work done by a person lifting a 240-newton bag of sugar 2 meters.

Find the area of the triangle having the indicated angle and sides. ​ B = 71°20', a = 62, c = 24 ​ (Round your answer to one decimal place.) ​

Find u + v. $\mathbf { u } = \langle 6,1 \rangle , \mathbf { v } = \langle 1,7 \rangle$

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form. $- 7 ( \sqrt { 3 } + i ) ^ { 5 }$

Use DeMoivre's Theorem to find the indicated power of the following complex number. $( - 3 + 3 i ) ^ { 4 }$

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place.

A traffic light weighing 15 pounds is suspended by two cables (see figure) .Find the tension in each cable if θ₁ = 40° and θ₂ = 35°.Approximate the answers to one decimal place.

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.)

Find the trigonometric form of $- 14 \sqrt { 3 } + 14 i$ .

Find the standard form of the complex number $10 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$ .Round values to the nearest hundredth.

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $9 \left( \cos 62 ^ { \circ } + i \sin 62 ^ { \circ } \right)$

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $14 \left( \cos \frac { 2 \pi } { 5 } + i \sin \frac { 2 \pi } { 5 } \right)$

Find the dot product of u and v. $\begin{array} { l } \mathbf { u } = \langle - 7,1 \rangle \\\mathbf { v } = \langle 4 , - 5 \rangle\end{array}$

Find the area of the triangle having the indicated angle and sides. B = 71°20', a = 62, c = 24 (Round your answer to one decimal place.)