Question 1

Find u - v. 
 $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 4 \mathbf { j }$

Accepted Answer

A)   $- 2 \mathbf { i } - 2 \mathbf { j }$ 
B)   $- 3 \mathbf { i } - 2 \mathbf { j }$ 
C)   $- 2 \mathbf { i } - 2 \mathbf { j }$. 
D)   $2 \mathbf { i } - 2 \mathbf { j }$ 
E)   $\mathrm { i } - \mathrm { j }$ 
A)   $- 2 \mathbf { i } - 2 \mathbf { j }$ 
B)   $- 3 \mathbf { i } - 2 \mathbf { j }$ 
C)   $- 2 \mathbf { i } - 2 \mathbf { j }$. 
D)   $2 \mathbf { i } - 2 \mathbf { j }$ 
E)   $\mathrm { i } - \mathrm { j }$

Question 2

Use the vectors $\mathbf { u } = \langle 3,5 \rangle$ , $\mathbf { v } = \langle - 2,4 \rangle$ , and $\mathbf { w } = \langle 3 , - 4 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar.
  $\left( \mathbf { v } ^ { * } \mathbf { u } \right) \mathbf { w }$

Accepted Answer

A)  $\langle 42 , - 60 \rangle$ ; vector 
B)  $\langle 42 , - 56 \rangle$ ; vector 
C) -58; scalar 
D) -56; scalar 
E)  $\langle 42 , - 52 \rangle$ ; vector 
A)  $\langle 42 , - 60 \rangle$ ; vector 
B)  $\langle 42 , - 56 \rangle$ ; vector 
C) -58; scalar 
D) -56; scalar 
E)  $\langle 42 , - 52 \rangle$ ; vector

Question 3

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. ​
A = 130°, a = 40, b = 25
​

Accepted Answer

A) B ≈ 11°, C ≈ 39°, c ≈ 20.05 
B) B ≈ 39°, C ≈ 11°, c ≈ 20.05 
C) B ≈ 28.61°, C ≈ 21.39°, c ≈ 19.05 
D) B ≈ 21.39°, C ≈ 28.61°, c ≈ 19.05 
E) No Solution 
A) B ≈ 11°, C ≈ 39°, c ≈ 20.05 
B) B ≈ 39°, C ≈ 11°, c ≈ 20.05 
C) B ≈ 28.61°, C ≈ 21.39°, c ≈ 19.05 
D) B ≈ 21.39°, C ≈ 28.61°, c ≈ 19.05 
E) No Solution

Question 4

Perform the operation shown below and leave the result in trigonometric form. $\left[ 4 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right) \right] \left[ 3 \left( \cos \frac { 3 \pi } { 7 } + i \sin \frac { 3 \pi } { 7 } \right) \right]$

Accepted Answer

A)  $7 \left( \cos \frac { 23 \pi } { 21 } + i \sin \frac { 23 \pi } { 21 } \right)$ 
B)   $12 \left( \cos \frac { 23 \pi } { 21 } + i \sin \frac { 23 \pi } { 21 } \right)$ 
C)   $12 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
D)   $12 \left( \cos \frac { 2 \pi } { 7 } + i \sin \frac { 2 \pi } { 7 } \right)$ 
E)   $7 \left( \cos \frac { 2 \pi } { 7 } + i \sin \frac { 2 \pi } { 7 } \right)$ 
A)  $7 \left( \cos \frac { 23 \pi } { 21 } + i \sin \frac { 23 \pi } { 21 } \right)$ 
B)   $12 \left( \cos \frac { 23 \pi } { 21 } + i \sin \frac { 23 \pi } { 21 } \right)$ 
C)   $12 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
D)   $12 \left( \cos \frac { 2 \pi } { 7 } + i \sin \frac { 2 \pi } { 7 } \right)$ 
E)   $7 \left( \cos \frac { 2 \pi } { 7 } + i \sin \frac { 2 \pi } { 7 } \right)$

Question 5

Let w be a vector with initial point (4, -4) and terminal point (2, 5).Write w as a linear combination of the standard unit vectors i and j.

Accepted Answer

A)   $\mathbf { w } = 8 \mathbf { i } - 3 \mathbf { j }$ 
B)   $\mathbf { w } = 0 \mathbf { i } + 3 \mathbf { j }$ 
C)   $\mathbf { w } = \mathbf { i } + 6 \mathbf { j }$ 
D)   $\mathbf { w } = - 2 \mathbf { i } + 9 \mathbf { j }$ 
E)   $\mathbf { w } = 6 \mathbf { i } - 9 \mathbf { j }$ 
A)   $\mathbf { w } = 8 \mathbf { i } - 3 \mathbf { j }$ 
B)   $\mathbf { w } = 0 \mathbf { i } + 3 \mathbf { j }$ 
C)   $\mathbf { w } = \mathbf { i } + 6 \mathbf { j }$ 
D)   $\mathbf { w } = - 2 \mathbf { i } + 9 \mathbf { j }$ 
E)   $\mathbf { w } = 6 \mathbf { i } - 9 \mathbf { j }$

Question 6

Write the complex number in trigonometric form.

Accepted Answer

A)  $Z = 2 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
B)   $Z = 2 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
C)   $Z = 2 \left( \cos \frac { 7 \pi } { 2 } + i \sin \frac { 7 \pi } { 2 } \right)$ 
D)   $Z = 2 \left( \cos \frac { \pi } { 2 } - i \sin \frac { \pi } { 2 } \right)$ 
E)   $Z = 2 \left( \cos \frac { 3 \pi } { 2 } - i \sin \frac { 3 \pi } { 2 } \right)$ 
A)  $Z = 2 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
B)   $Z = 2 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
C)   $Z = 2 \left( \cos \frac { 7 \pi } { 2 } + i \sin \frac { 7 \pi } { 2 } \right)$ 
D)   $Z = 2 \left( \cos \frac { \pi } { 2 } - i \sin \frac { \pi } { 2 } \right)$ 
E)   $Z = 2 \left( \cos \frac { 3 \pi } { 2 } - i \sin \frac { 3 \pi } { 2 } \right)$

Question 7

Find the fourth roots of $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i$ Write the roots in trigonometric form.

Accepted Answer

A)  $\begin{array} { l } 
w _ { 1 } = \cos \left( 20 ^ { \circ } \right) + i \sin \left( 20 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 110 ^ { \circ } \right) + i \sin \left( 110 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 200 ^ { \circ } \right) + i \sin \left( 200 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 290 ^ { \circ } \right) + i \sin \left( 290 ^ { \circ } \right)
\end{array}$ 
B)  $\begin{array} { l } 
w _ { 1 } = \cos \left( 30 ^ { \circ } \right) + i \sin \left( 30 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 120 ^ { \circ } \right) + i \sin \left( 120 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 210 ^ { \circ } \right) + i \sin \left( 210 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 300 ^ { \circ } \right) + i \sin \left( 300 ^ { \circ } \right)
\end{array}$ 
C)  $\begin{array} { l } 
w _ { 1 } = \cos \left( 35 ^ { \circ } \right) + i \sin \left( 35 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 125 ^ { \circ } \right) + i \sin \left( 125 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 215 ^ { \circ } \right) + i \sin \left( 215 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 305 ^ { \circ } \right) + i \sin \left( 305 ^ { \circ } \right)
\end{array}$ 
D)  $\begin{array} { l } 
w _ { 1 } = \cos \left( 25 ^ { \circ } \right) + i \sin \left( 25 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 115 ^ { \circ } \right) + i \sin \left( 115 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 205 ^ { \circ } \right) + i \sin \left( 205 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 295 ^ { \circ } \right) + i \sin \left( 295 ^ { \circ } \right)
\end{array}$ 
E)  $\begin{array} { l } 
w _ { 1 } = \cos \left( 40 ^ { \circ } \right) + i \sin \left( 40 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 130 ^ { \circ } \right) + i \sin \left( 130 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 220 ^ { \circ } \right) + i \sin \left( 220 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 310 ^ { \circ } \right) + i \sin \left( 310 ^ { \circ } \right)
\end{array}$ 
A)  $\begin{array} { l } 
w _ { 1 } = \cos \left( 20 ^ { \circ } \right) + i \sin \left( 20 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 110 ^ { \circ } \right) + i \sin \left( 110 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 200 ^ { \circ } \right) + i \sin \left( 200 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 290 ^ { \circ } \right) + i \sin \left( 290 ^ { \circ } \right)
\end{array}$ 
B)  $\begin{array} { l } 
w _ { 1 } = \cos \left( 30 ^ { \circ } \right) + i \sin \left( 30 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 120 ^ { \circ } \right) + i \sin \left( 120 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 210 ^ { \circ } \right) + i \sin \left( 210 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 300 ^ { \circ } \right) + i \sin \left( 300 ^ { \circ } \right)
\end{array}$ 
C)  $\begin{array} { l } 
w _ { 1 } = \cos \left( 35 ^ { \circ } \right) + i \sin \left( 35 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 125 ^ { \circ } \right) + i \sin \left( 125 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 215 ^ { \circ } \right) + i \sin \left( 215 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 305 ^ { \circ } \right) + i \sin \left( 305 ^ { \circ } \right)
\end{array}$ 
D)  $\begin{array} { l } 
w _ { 1 } = \cos \left( 25 ^ { \circ } \right) + i \sin \left( 25 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 115 ^ { \circ } \right) + i \sin \left( 115 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 205 ^ { \circ } \right) + i \sin \left( 205 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 295 ^ { \circ } \right) + i \sin \left( 295 ^ { \circ } \right)
\end{array}$ 
E)  $\begin{array} { l } 
w _ { 1 } = \cos \left( 40 ^ { \circ } \right) + i \sin \left( 40 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 130 ^ { \circ } \right) + i \sin \left( 130 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 220 ^ { \circ } \right) + i \sin \left( 220 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 310 ^ { \circ } \right) + i \sin \left( 310 ^ { \circ } \right)
\end{array}$

Question 8

Divide the complex numbers below and leave the result in trigonometric form. $\frac { 4 ( \cos ( 7 \pi / 10 ) + i \sin ( 7 \pi / 10 ) ) } { 10 ( \cos ( 3 \pi / 7 ) + i \sin ( 3 \pi / 7 ) ) }$

Accepted Answer

A)  $\cos \frac { 79 } { 70 } \pi + i \sin \frac { 79 } { 70 } \pi$ 
B)   $\cos \frac { 19 } { 70 } \pi + i \sin \frac { 19 } { 70 } \pi$ 
C)   $\frac { 2 } { 5 } \left( \cos \frac { 79 } { 70 } \pi + i \sin \frac { 79 } { 70 } \pi \right)$ 
D)   $\frac { 2 } { 5 } \left( \cos \frac { 2 } { 35 } \pi + i \sin \frac { 2 } { 35 } \pi \right)$ 
E)   $\frac { 2 } { 5 } \left( \cos \frac { 19 } { 70 } \pi + i \sin \frac { 19 } { 70 } \pi \right)$ 
A)  $\cos \frac { 79 } { 70 } \pi + i \sin \frac { 79 } { 70 } \pi$ 
B)   $\cos \frac { 19 } { 70 } \pi + i \sin \frac { 19 } { 70 } \pi$ 
C)   $\frac { 2 } { 5 } \left( \cos \frac { 79 } { 70 } \pi + i \sin \frac { 79 } { 70 } \pi \right)$ 
D)   $\frac { 2 } { 5 } \left( \cos \frac { 2 } { 35 } \pi + i \sin \frac { 2 } { 35 } \pi \right)$ 
E)   $\frac { 2 } { 5 } \left( \cos \frac { 19 } { 70 } \pi + i \sin \frac { 19 } { 70 } \pi \right)$

Question 9

Find the area of the triangle having the indicated angle and sides. ​
С = 84°34', a = 16, b = 26
​
(Round your answer to one decimal place.)
​

Accepted Answer

A) 209.1 
B) ​207.1 
C) ​208.1 
D) ​206.1 
E) ​414.1 
A) 209.1 
B) ​207.1 
C) ​208.1 
D) ​206.1 
E) ​414.1

Question 10

Determine whether u are v and orthogonal, parallel, or neither. $\mathbf { u } = \langle - 1,5 \rangle , \mathbf { v } = \langle - 10 , - 3 \rangle$

Accepted Answer

A) neither 
B) orthogonal 
C) parallel 
A) neither 
B) orthogonal 
C) parallel

Question 11

Represent the complex number graphically, and find the trigonometric form of the number.  
-8i

Accepted Answer

A)    $8 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
B)     $8 ( \cos \pi - i \sin \pi )$ 
C)     $8 \left( \cos \frac { 3 \pi } { 2 } - i \sin \frac { 3 \pi } { 2 } \right)$ 
D)    $8 ( \cos \pi + i \sin \pi )$ 
E)    $8 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
A)    $8 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
B)     $8 ( \cos \pi - i \sin \pi )$ 
C)     $8 \left( \cos \frac { 3 \pi } { 2 } - i \sin \frac { 3 \pi } { 2 } \right)$ 
D)    $8 ( \cos \pi + i \sin \pi )$ 
E)    $8 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$

Question 12

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 = 20, b = 22, c = 16
​

Accepted Answer

A) Law of Cosines; No solution 
B) Law of Cosines; A ≈ 61.12°, B ≈ 74.41°, C ≈ 44.47° 
C) Law of Sines; No solution 
D) Law of Sines; A ≈ 61.12°, B ≈ 44.47°, C ≈ 74.41° 
E) Law of Sines; A ≈ 61.12°, B ≈ 74.41°, C ≈ 44.47° 
A) Law of Cosines; No solution 
B) Law of Cosines; A ≈ 61.12°, B ≈ 74.41°, C ≈ 44.47° 
C) Law of Sines; No solution 
D) Law of Sines; A ≈ 61.12°, B ≈ 44.47°, C ≈ 74.41° 
E) Law of Sines; A ≈ 61.12°, B ≈ 74.41°, C ≈ 44.47°

Question 13

Find a unit vector in the direction of the given vector.  $\mathbf { w } = 5 \mathbf { j }$

Accepted Answer

A) j 
B) i 
C) - j 
D) - i 
E)  i - j 
A) j 
B) i 
C) - j 
D) - i 
E)  i - j

Question 14

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. ​
A = 3.08, b = 0.78, c = 2.48
​

Accepted Answer

A) 3.5 
B) 0.1 
C) 0.4 
D) 0.2 
E) 0.7 
A) 3.5 
B) 0.1 
C) 0.4 
D) 0.2 
E) 0.7

Question 15

Determine $\text { u v }$ if $\| \mathbf { u } \| = 5$ , $\| \mathbf { v } \| = 4$ , and $\theta = \frac { \pi } { 4 }$ where $\theta$ is the angle between u and v.Round answer to two decimal places.

Accepted Answer

A) 15.73 
B) 12.07 
C) 10.00 
D) 17.32 
E) 14.14 
A) 15.73 
B) 12.07 
C) 10.00 
D) 17.32 
E) 14.14

Question 16

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage, I represents current, and Z represents impedance (a measure of opposition to a sinusoidal electric current), is used in electrical engineering.The variable is a complex number.   $\begin{array} { l } 
I = 13 + 5 i \
Z = 4 + 3 i
\end{array}$

Accepted Answer

A)  $37 + 59 i$ 
B)   $37 - 37 i$ 
C)   $59 - 37 i$ 
D)   $37 - 59 i$ 
E)  $59 + 37 i$ 
A)  $37 + 59 i$ 
B)   $37 - 37 i$ 
C)   $59 - 37 i$ 
D)   $37 - 59 i$ 
E)  $59 + 37 i$

Question 17

Find the trigonometric form of $- 5 + 5 \sqrt { 3 } i$ .

Accepted Answer

A)  $5 \sqrt { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
B)   $5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
C)   $5 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
D)   $10 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
E)   $10 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
A)  $5 \sqrt { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
B)   $5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
C)   $5 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
D)   $10 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
E)   $10 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$

Question 18

Use the dot product to find the magnitude of u.  
  $\mathbf { u } = \langle - 7,12 \rangle$

Accepted Answer

A)  $3 \sqrt { 21 }$ 
B)  $\sqrt { 195 }$ 
C)  $\sqrt { 197 }$ 
D)  $\sqrt { 193 }$ 
E)  $\sqrt { 191 }$ 
A)  $3 \sqrt { 21 }$ 
B)  $\sqrt { 195 }$ 
C)  $\sqrt { 197 }$ 
D)  $\sqrt { 193 }$ 
E)  $\sqrt { 191 }$

Question 19

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. ​
C = 64.47°, a = 39, c = 50
​

Accepted Answer

A) A ≈ 70.79°, B ≈ 44.74°, b ≈ 52.32 
B) A ≈ 70.53°, B ≈ 45°, b ≈ 50 
C) A ≈ 44.74°, B ≈ 70.79°, b ≈ 52.32 
D) A ≈ 45°, B ≈ 70.53°, b ≈ 50 
E) No Solution 
A) A ≈ 70.79°, B ≈ 44.74°, b ≈ 52.32 
B) A ≈ 70.53°, B ≈ 45°, b ≈ 50 
C) A ≈ 44.74°, B ≈ 70.79°, b ≈ 52.32 
D) A ≈ 45°, B ≈ 70.53°, b ≈ 50 
E) No Solution

Question 20

Perform the operation and leave the result in trigonometric form.   $\left( \cos 80 ^ { \circ } + i \sin 80 ^ { \circ } \right) \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$

Accepted Answer

A)  $\cos 50 ^ { \circ } - i \sin 50 ^ { \circ }$ 
B)   $\frac { 1 } { 2 } \left( \cos 50 ^ { \circ } - i \sin 50 ^ { \circ } \right)$ 
C)   $\frac { 1 } { 2 } \left( \cos 80 ^ { \circ } + i \sin 80 ^ { \circ } \right)$ 
D)   $\frac { 1 } { 2 } \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right)$ 
E)   $\cos 50 ^ { \circ } + i \sin 50 ^ { \circ }$ 
A)  $\cos 50 ^ { \circ } - i \sin 50 ^ { \circ }$ 
B)   $\frac { 1 } { 2 } \left( \cos 50 ^ { \circ } - i \sin 50 ^ { \circ } \right)$ 
C)   $\frac { 1 } { 2 } \left( \cos 80 ^ { \circ } + i \sin 80 ^ { \circ } \right)$ 
D)   $\frac { 1 } { 2 } \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right)$ 
E)   $\cos 50 ^ { \circ } + i \sin 50 ^ { \circ }$

Find u - v. $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 4 \mathbf { j }$

Use the vectors $\mathbf { u } = \langle 3,5 \rangle$ , $\mathbf { v } = \langle - 2,4 \rangle$ , and $\mathbf { w } = \langle 3 , - 4 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $\left( \mathbf { v } ^ { * } \mathbf { u } \right) \mathbf { w }$

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. A = 130°, a = 40, b = 25

Perform the operation shown below and leave the result in trigonometric form. $\left[ 4 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right) \right] \left[ 3 \left( \cos \frac { 3 \pi } { 7 } + i \sin \frac { 3 \pi } { 7 } \right) \right]$

Let w be a vector with initial point (4, -4) and terminal point (2, 5).Write w as a linear combination of the standard unit vectors i and j.

Write the complex number in trigonometric form.

Find the fourth roots of $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i$ Write the roots in trigonometric form.

Divide the complex numbers below and leave the result in trigonometric form. $\frac { 4 ( \cos ( 7 \pi / 10 ) + i \sin ( 7 \pi / 10 ) ) } { 10 ( \cos ( 3 \pi / 7 ) + i \sin ( 3 \pi / 7 ) ) }$

Find the area of the triangle having the indicated angle and sides. С = 84°34', a = 16, b = 26 (Round your answer to one decimal place.)

Determine whether u are v and orthogonal, parallel, or neither. $\mathbf { u } = \langle - 1,5 \rangle , \mathbf { v } = \langle - 10 , - 3 \rangle$

Represent the complex number graphically, and find the trigonometric form of the number. -8i

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 = 20, b = 22, c = 16

Find a unit vector in the direction of the given vector. $\mathbf { w } = 5 \mathbf { j }$

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. A = 3.08, b = 0.78, c = 2.48

Determine $\text { u v }$ if $\| \mathbf { u } \| = 5$ , $\| \mathbf { v } \| = 4$ , and $\theta = \frac { \pi } { 4 }$ where $\theta$ is the angle between u and v.Round answer to two decimal places.

Find the trigonometric form of $- 5 + 5 \sqrt { 3 } i$ .

Use the dot product to find the magnitude of u. $\mathbf { u } = \langle - 7,12 \rangle$

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. C = 64.47°, a = 39, c = 50

Perform the operation and leave the result in trigonometric form. $\left( \cos 80 ^ { \circ } + i \sin 80 ^ { \circ } \right) \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$

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Exam 6: Additional Topics In Trigonometery

Find u - v. u=−3i+2j,v=4j\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 4 \mathbf { j }u=−3i+2j,v=4j

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. ​ A = 130°, a = 40, b = 25 ​

Let w be a vector with initial point (4, -4) and terminal point (2, 5).Write w as a linear combination of the standard unit vectors i and j.

Write the complex number in trigonometric form.

Find the fourth roots of −12+32i- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i−21​+23​​i Write the roots in trigonometric form.

Find the area of the triangle having the indicated angle and sides. ​ С = 84°34', a = 16, b = 26 ​ (Round your answer to one decimal place.) ​

Determine whether u are v and orthogonal, parallel, or neither. u=⟨−1,5⟩,v=⟨−10,−3⟩\mathbf { u } = \langle - 1,5 \rangle , \mathbf { v } = \langle - 10 , - 3 \rangleu=⟨−1,5⟩,v=⟨−10,−3⟩

Represent the complex number graphically, and find the trigonometric form of the number. -8i

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 = 20, b = 22, c = 16 ​

Find a unit vector in the direction of the given vector. w=5j\mathbf { w } = 5 \mathbf { j }w=5j

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. ​ A = 3.08, b = 0.78, c = 2.48 ​

Determine u v \text { u v } u v if ∥u∥=5\| \mathbf { u } \| = 5∥u∥=5 , ∥v∥=4\| \mathbf { v } \| = 4∥v∥=4 , and θ=π4\theta = \frac { \pi } { 4 }θ=4π​ where θ\thetaθ is the angle between u and v.Round answer to two decimal places.

Find the trigonometric form of −5+53i- 5 + 5 \sqrt { 3 } i−5+53​i .

Use the dot product to find the magnitude of u. u=⟨−7,12⟩\mathbf { u } = \langle - 7,12 \rangleu=⟨−7,12⟩

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. ​ C = 64.47°, a = 39, c = 50 ​

Perform the operation and leave the result in trigonometric form. (cos⁡80∘+isin⁡80∘)(cos⁡330∘+isin⁡330∘)\left( \cos 80 ^ { \circ } + i \sin 80 ^ { \circ } \right) \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)(cos80∘+isin80∘)(cos330∘+isin330∘)

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

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Find u - v. $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 4 \mathbf { j }$

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. A = 130°, a = 40, b = 25

Find the fourth roots of $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i$ Write the roots in trigonometric form.

Find the area of the triangle having the indicated angle and sides. С = 84°34', a = 16, b = 26 (Round your answer to one decimal place.)

Determine whether u are v and orthogonal, parallel, or neither. $\mathbf { u } = \langle - 1,5 \rangle , \mathbf { v } = \langle - 10 , - 3 \rangle$

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 = 20, b = 22, c = 16

Find a unit vector in the direction of the given vector. $\mathbf { w } = 5 \mathbf { j }$

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. A = 3.08, b = 0.78, c = 2.48

Determine $\text { u v }$ if $\| \mathbf { u } \| = 5$ , $\| \mathbf { v } \| = 4$ , and $\theta = \frac { \pi } { 4 }$ where $\theta$ is the angle between u and v.Round answer to two decimal places.

Find the trigonometric form of $- 5 + 5 \sqrt { 3 } i$ .

Use the dot product to find the magnitude of u. $\mathbf { u } = \langle - 7,12 \rangle$

Use the Law of Sines to solve (if possible) the triangle.If two solutions exist, find both.Round your answers to two decimal places. C = 64.47°, a = 39, c = 50

Perform the operation and leave the result in trigonometric form. $\left( \cos 80 ^ { \circ } + i \sin 80 ^ { \circ } \right) \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$