Question 1

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi.
-$( 1 + i ) ^ { 20 }$

Accepted Answer

A)  $- 1024 i$ 
B)  1024 
C)  $1024 \mathrm { i }$ 
D)  $- 1024$ 
A)  $- 1024 i$ 
B)  1024 
C)  $1024 \mathrm { i }$ 
D)  $- 1024$

Question 2

Solve the problem.
-One rope pulls a barge directly east with a force of 83 N, and another rope pulls the barge directly north with a force of 47 N. Find the magnitude of the resultant force acting on the barge.

Accepted Answer

A)  95 N 
B)  3901 N 
C)  36 N 
D)  130 N 
A)  95 N 
B)  3901 N 
C)  36 N 
D)  130 N

Question 3

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.
-Let $\mathbf { u } = \langle 1,5 \rangle$. Find the unit vector in the direction of $\mathbf { u }$, and write your answer as a linear combination of the standard unit vectors $\mathbf { i }$ and $\mathbf { j }$.

Accepted Answer

A)  $\frac { 1 } { \sqrt { 26 } } \mathrm { i } + \frac { 5 } { \sqrt { 26 } } \mathrm { j }$ 
B)  $\mathrm { i } + \mathrm { j }$ 
C)  $\frac { 1 } { 6 } \mathrm { i } + \frac { 5 } { 6 } \mathrm { j }$ 
D)  $\frac { 1 } { 26 } \mathbf { i } + \frac { 5 } { 26 } \mathrm { j }$ 
A)  $\frac { 1 } { \sqrt { 26 } } \mathrm { i } + \frac { 5 } { \sqrt { 26 } } \mathrm { j }$ 
B)  $\mathrm { i } + \mathrm { j }$ 
C)  $\frac { 1 } { 6 } \mathrm { i } + \frac { 5 } { 6 } \mathrm { j }$ 
D)  $\frac { 1 } { 26 } \mathbf { i } + \frac { 5 } { 26 } \mathrm { j }$

Question 4

Solve the problem.
-Find the length of each petal of the polar curve $r = 8 - 3 \sin 4 \theta$. Note that this means the distance from the pole to the farthest point on the petal, not the arc length.

Accepted Answer

A)  3 
B)  5 
C)  8 
D)  11 
A)  3 
B)  5 
C)  8 
D)  11

Question 5

Find a polar equation for the parametric equations $x = 5 \cos ^ { 2 } \theta , y = 5 \cos \theta \sin \theta$

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = 25 \cos ^ { 2 } \theta$ 
B)  $r = 5 \cos \theta$ 
C)  $r = 5 \sin \theta$ 
D)  $y = x \tan \theta$ 
A)  $x ^ { 2 } + y ^ { 2 } = 25 \cos ^ { 2 } \theta$ 
B)  $r = 5 \cos \theta$ 
C)  $r = 5 \sin \theta$ 
D)  $y = x \tan \theta$

Question 6

Solve the problem using a graphing calculator.
-Determine whether a baseball hit 109 feet per second at an angle of $30 ^ { \circ }$ relative to level ground will clear a 10-foot wall 400 feet away.

Accepted Answer

A) True 
 B)False

Question 7

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0°, 360°) rounded to the nearest tenth.
-$\langle - 5,7 \rangle$

Accepted Answer

A)  $\sqrt { 74 } , 144.5 ^ { \circ }$ 
B)  $\sqrt { 74 } , 35.5 ^ { \circ }$ 
C)  $\sqrt { 74 } , 125.5 ^ { \circ }$ 
D)  $\sqrt { 74 } , 54.5 ^ { \circ }$ 
A)  $\sqrt { 74 } , 144.5 ^ { \circ }$ 
B)  $\sqrt { 74 } , 35.5 ^ { \circ }$ 
C)  $\sqrt { 74 } , 125.5 ^ { \circ }$ 
D)  $\sqrt { 74 } , 54.5 ^ { \circ }$

Question 8

Use your grapher to determine which of the graphs matches the given polar equation.
-$$r = 4 \sin \theta$$

Accepted Answer

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

Question 9

Express the indicated roots of unity in standard form a + bi.
-Tenth roots of unity

Accepted Answer

A)  $ 1+0 \mathrm{i} $
$$
\begin{array}{l}
\cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \
\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \
\cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i \
\cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \
\cos \pi+i \sin \pi=-1+0 i \
\cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i \
\cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i \
\cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i \
\cos \frac{9 \pi}{5}+i \sin \frac{9 \pi}{5} \approx 0.81-0.59 i
\end{array}
$$ 
B)  $ 1+0 i $
$ \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i $
$ \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i $
$ 0+i $
$ \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i $
$ \cos \pi+i \sin \pi=-1+0 i $
$ \cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i $
$ \cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i $
$ \cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i $
$ 0-i $ 
C)  $ 1+0 i $
$$
\begin{array}{l}
\cos \frac{\pi}{10}+i \sin \frac{\pi}{10} \approx 0.95+0.31 i \
\cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \
\cos \frac{3 \pi}{10}+i \sin \frac{3 \pi}{10} \approx 0.59+0.81 i \
\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \
\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}=0+i \
\cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i \
\cos \frac{7 \pi}{10}+i \sin \frac{7 \pi}{10} \approx-0.59+0.81 i \
\cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \
\cos \frac{9 \pi}{10}+i \sin \frac{9 \pi}{10} \approx-0.95+0.31 i
\end{array}
$$ 
D)  $ 1+0 i $
$ \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i $
$ \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i $
$ \cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i $
$ \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i $
$ \cos \pi+i \sin \pi=-1+0 i $
$ \cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i $
$ \cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i $
$ \cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i $
$ 0-i $ 
A)  $ 1+0 \mathrm{i} $
$$
\begin{array}{l}
\cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \
\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \
\cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i \
\cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \
\cos \pi+i \sin \pi=-1+0 i \
\cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i \
\cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i \
\cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i \
\cos \frac{9 \pi}{5}+i \sin \frac{9 \pi}{5} \approx 0.81-0.59 i
\end{array}
$$ 
B)  $ 1+0 i $
$ \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i $
$ \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i $
$ 0+i $
$ \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i $
$ \cos \pi+i \sin \pi=-1+0 i $
$ \cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i $
$ \cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i $
$ \cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i $
$ 0-i $ 
C)  $ 1+0 i $
$$
\begin{array}{l}
\cos \frac{\pi}{10}+i \sin \frac{\pi}{10} \approx 0.95+0.31 i \
\cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \
\cos \frac{3 \pi}{10}+i \sin \frac{3 \pi}{10} \approx 0.59+0.81 i \
\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \
\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}=0+i \
\cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i \
\cos \frac{7 \pi}{10}+i \sin \frac{7 \pi}{10} \approx-0.59+0.81 i \
\cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \
\cos \frac{9 \pi}{10}+i \sin \frac{9 \pi}{10} \approx-0.95+0.31 i
\end{array}
$$ 
D)  $ 1+0 i $
$ \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i $
$ \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i $
$ \cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i $
$ \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i $
$ \cos \pi+i \sin \pi=-1+0 i $
$ \cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i $
$ \cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i $
$ \cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i $
$ 0-i $

Question 10

Express the indicated roots of unity in standard form a + bi.
-Ninth roots of unity

Accepted Answer

A)  $ 1+0 \mathrm{i} $
$$
\begin{array}{l}
\cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i \
\cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i \
\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} \
\cos \frac{8 \pi}{9}+i \sin \frac{8 \pi}{9} \approx-0.94+0.34 i \
\cos \frac{10 \pi}{9}+i \sin \frac{10 \pi}{9} \approx-0.94-0.34 i \
\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.50-i \frac{\sqrt{3}}{2} \
\cos \frac{14 \pi}{9}+i \sin \frac{14 \pi}{9} \approx 0.17-0.98 \mathrm{i} \
1-i
\end{array}
$$ 
B)  $ 1+0 \mathrm{i} $
$$
\begin{array}{l}
\cos \frac{\pi}{9}+i \sin \frac{\pi}{9} \approx 0.94+0.34 i \
\cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i \
\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}=0.50+i \frac{\sqrt{3}}{2} \
\cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i \
\cos \frac{5 \pi}{9}+i \sin \frac{5 \pi}{9} \approx-0.17+0.98 i \
\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} \
\cos \frac{7 \pi}{9}+i \sin \frac{7 \pi}{9} \approx-0.77+0.64 i \
\cos \frac{8 \pi}{9}+i \sin \frac{8 \pi}{9} \approx-0.94+0.34 i
\end{array}
$$ 
C)  $ 1+0 i $
$ \cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i $
$ \cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i $
$ \cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} $
$ \cos \frac{8 \pi}{9}+i \sin \frac{8 \pi}{9} \approx-0.94+0.34 i $
$ \cos \frac{10 \pi}{9}+i \sin \frac{10 \pi}{9} \approx-0.94-0.34 i $
$ \cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.50-i \frac{\sqrt{3}}{2} $
$ \cos \frac{14 \pi}{9}+i \sin \frac{14 \pi}{9} \approx 0.17-0.98 i $
$ \cos \frac{16 \pi}{9}+i \sin \frac{16 \pi}{9} \approx 0.77-0.64 i $ 
D)  $ 1+0 i $
$ \cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i $
$ \cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i $
$ \cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} $
$ -1+0 i $
$ \cos \frac{10 \pi}{9}+i \sin \frac{10 \pi}{9} \approx-0.94-0.34 i $
$ \cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.50-i \frac{\sqrt{3}}{2} $
$ \cos \frac{14 \pi}{9}+i \sin \frac{14 \pi}{9} \approx 0.17-0.98 i $
$ \cos \frac{16 \pi}{9}+i \sin \frac{16 \pi}{9} \approx 0.77-0.64 i $ 
A)  $ 1+0 \mathrm{i} $
$$
\begin{array}{l}
\cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i \
\cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i \
\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} \
\cos \frac{8 \pi}{9}+i \sin \frac{8 \pi}{9} \approx-0.94+0.34 i \
\cos \frac{10 \pi}{9}+i \sin \frac{10 \pi}{9} \approx-0.94-0.34 i \
\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.50-i \frac{\sqrt{3}}{2} \
\cos \frac{14 \pi}{9}+i \sin \frac{14 \pi}{9} \approx 0.17-0.98 \mathrm{i} \
1-i
\end{array}
$$ 
B)  $ 1+0 \mathrm{i} $
$$
\begin{array}{l}
\cos \frac{\pi}{9}+i \sin \frac{\pi}{9} \approx 0.94+0.34 i \
\cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i \
\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}=0.50+i \frac{\sqrt{3}}{2} \
\cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i \
\cos \frac{5 \pi}{9}+i \sin \frac{5 \pi}{9} \approx-0.17+0.98 i \
\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} \
\cos \frac{7 \pi}{9}+i \sin \frac{7 \pi}{9} \approx-0.77+0.64 i \
\cos \frac{8 \pi}{9}+i \sin \frac{8 \pi}{9} \approx-0.94+0.34 i
\end{array}
$$ 
C)  $ 1+0 i $
$ \cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i $
$ \cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i $
$ \cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} $
$ \cos \frac{8 \pi}{9}+i \sin \frac{8 \pi}{9} \approx-0.94+0.34 i $
$ \cos \frac{10 \pi}{9}+i \sin \frac{10 \pi}{9} \approx-0.94-0.34 i $
$ \cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.50-i \frac{\sqrt{3}}{2} $
$ \cos \frac{14 \pi}{9}+i \sin \frac{14 \pi}{9} \approx 0.17-0.98 i $
$ \cos \frac{16 \pi}{9}+i \sin \frac{16 \pi}{9} \approx 0.77-0.64 i $ 
D)  $ 1+0 i $
$ \cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i $
$ \cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i $
$ \cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} $
$ -1+0 i $
$ \cos \frac{10 \pi}{9}+i \sin \frac{10 \pi}{9} \approx-0.94-0.34 i $
$ \cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.50-i \frac{\sqrt{3}}{2} $
$ \cos \frac{14 \pi}{9}+i \sin \frac{14 \pi}{9} \approx 0.17-0.98 i $
$ \cos \frac{16 \pi}{9}+i \sin \frac{16 \pi}{9} \approx 0.77-0.64 i $

Question 11

Find a· b.
-$$a = 6 \mathbf { j } , \quad b = i + 5 j$$

Accepted Answer

A)  $\langle 1,30 \rangle$ 
B)  $- 30$ 
C)  $\langle 0,30 \rangle$ 
D)  30 
A)  $\langle 1,30 \rangle$ 
B)  $- 30$ 
C)  $\langle 0,30 \rangle$ 
D)  30

Question 12

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°.
-$( 4 \sqrt { 3 } , 12 )$

Accepted Answer

A)  $\left( 8 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 12 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
B)  $\left( 8 \sqrt { 3 } , 300 ^ { \circ } \right) , \left( - 8 \sqrt { 3 } , 60 ^ { \circ } \right)$ 
C)  $\left( 8 \sqrt { 3 } , 60 ^ { \circ } \right) , \left( - 8 \sqrt { 3 } , 240 ^ { \circ } \right)$ 
D)  $\left( 8 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 8 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
A)  $\left( 8 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 12 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
B)  $\left( 8 \sqrt { 3 } , 300 ^ { \circ } \right) , \left( - 8 \sqrt { 3 } , 60 ^ { \circ } \right)$ 
C)  $\left( 8 \sqrt { 3 } , 60 ^ { \circ } \right) , \left( - 8 \sqrt { 3 } , 240 ^ { \circ } \right)$ 
D)  $\left( 8 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 8 \sqrt { 3 } , 330 ^ { \circ } \right)$

Question 13

With your calculator set to radian mode and polar graphics capability, graph the following function in the window specified.
-$\mathrm { r } = \cos \theta + \sin \theta , 0 \leq \theta \leq 2 \pi , [ - 2,2 ]$ by $[ - 2,2 ]$

Accepted Answer

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

Question 14

Find the indicated roots. Write the answer in a + bi form.
-Cube roots of $8 \mathrm { i }$

Accepted Answer

A)  $- 2 i , \sqrt { 3 } + i , - \sqrt { 3 } + i$ 
B)  $2 i , \sqrt { 3 } - i , - \sqrt { 3 } - i$ 
C)  $2 i , \sqrt { 3 } + i , - \sqrt { 3 } + i$ 
D)  $- 2 i , - \sqrt { 3 } - i , \sqrt { 3 } - i$ 
A)  $- 2 i , \sqrt { 3 } + i , - \sqrt { 3 } + i$ 
B)  $2 i , \sqrt { 3 } - i , - \sqrt { 3 } - i$ 
C)  $2 i , \sqrt { 3 } + i , - \sqrt { 3 } + i$ 
D)  $- 2 i , - \sqrt { 3 } - i , \sqrt { 3 } - i$

Question 15

Plot the point with the given polar coordinates.
-$\left( 2,0 ^ { \circ } \right)$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 16

Solve the problem.
-What is the minimum force required to prevent a ball weighing $16.6 \mathrm { lb }$ from rolling down a ramp which is inclined $28.6 ^ { \circ }$ with the horizontal?

Accepted Answer

A)  $14.6 \mathrm { lb }$ 
B)  $7.3 \mathrm { lb }$ 
C)  $4 \mathrm { lb }$ 
D)  $7.9 \mathrm { lb }$ 
A)  $14.6 \mathrm { lb }$ 
B)  $7.3 \mathrm { lb }$ 
C)  $4 \mathrm { lb }$ 
D)  $7.9 \mathrm { lb }$

Question 17

Express the complex number in polar form.
-$- 4$

Accepted Answer

A)  $4 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right)$ 
B)  $4 \left( \cos 270 ^ { \circ } + \mathrm { i } \sin 270 ^ { \circ } \right)$ 
C)  $4 \left( \cos 0 ^ { \circ } + i \sin 0 ^ { \circ } \right)$ 
D)  $4 \left( \cos 90 ^ { \circ } + \mathrm { i } \sin 90 ^ { \circ } \right)$ 
A)  $4 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right)$ 
B)  $4 \left( \cos 270 ^ { \circ } + \mathrm { i } \sin 270 ^ { \circ } \right)$ 
C)  $4 \left( \cos 0 ^ { \circ } + i \sin 0 ^ { \circ } \right)$ 
D)  $4 \left( \cos 90 ^ { \circ } + \mathrm { i } \sin 90 ^ { \circ } \right)$

Question 18

Find a polar equation for the parametric equations.
$$x = f _ { 1 } ( \theta ) , y = f _ { 2 } ( \theta )$$

Accepted Answer

A)  $y = x \tan \theta$ 
B)  $r = \sqrt { \left[ f _ { 1 } ( \theta ) \right] ^ { 2 } + \left[ f _ { 2 } ( \theta ) \right] ^ { 2 } }$ 
C)  $x ^ { 2 } + y ^ { 2 } = \left[ f _ { 1 } ( \theta ) \right] ^ { 2 } + \left[ f _ { 2 } ( \theta ) \right] ^ { 2 }$ 
D)  $r = \left[ f _ { 1 } ( \theta ) \right] ^ { 2 } + \left[ f _ { 2 } ( \theta ) \right] ^ { 2 }$ 
A)  $y = x \tan \theta$ 
B)  $r = \sqrt { \left[ f _ { 1 } ( \theta ) \right] ^ { 2 } + \left[ f _ { 2 } ( \theta ) \right] ^ { 2 } }$ 
C)  $x ^ { 2 } + y ^ { 2 } = \left[ f _ { 1 } ( \theta ) \right] ^ { 2 } + \left[ f _ { 2 } ( \theta ) \right] ^ { 2 }$ 
D)  $r = \left[ f _ { 1 } ( \theta ) \right] ^ { 2 } + \left[ f _ { 2 } ( \theta ) \right] ^ { 2 }$

Question 19

Use the given graph to find the values of t that produce the graph in the given quadrant.
-$x=3-|t|, y=t-2,-6 \leq t \leq 6$
 
Quadrant I

Accepted Answer

A)  $- 3 \leq t \leq 2$ 
B)  $2 \leq t \leq 3$ 
C)  $3 \leq t \leq 6$ 
D)  $- 6 \leq \mathrm { t } \leq - 3$ 
A)  $- 3 \leq t \leq 2$ 
B)  $2 \leq t \leq 3$ 
C)  $3 \leq t \leq 6$ 
D)  $- 6 \leq \mathrm { t } \leq - 3$

Question 20

Find an equivalent equation in polar coordinates.
-$$x ^ { 2 } + y ^ { 2 } = 100$$

Accepted Answer

A)  $r = 10 \cos \theta$ 
B)  $r = 100$ 
C)  $r = 10 \sin \theta$ 
D)  $r = 10$ 
A)  $r = 10 \cos \theta$ 
B)  $r = 100$ 
C)  $r = 10 \sin \theta$ 
D)  $r = 10$

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi. - $( 1 + i ) ^ { 20 }$

Solve the problem. -One rope pulls a barge directly east with a force of 83 N, and another rope pulls the barge directly north with a force of 47 N. Find the magnitude of the resultant force acting on the barge.

Solve the problem. -Find the length of each petal of the polar curve $r = 8 - 3 \sin 4 \theta$ . Note that this means the distance from the pole to the farthest point on the petal, not the arc length.

Find a polar equation for the parametric equations $x = 5 \cos ^ { 2 } \theta , y = 5 \cos \theta \sin \theta$

Solve the problem using a graphing calculator. -Determine whether a baseball hit 109 feet per second at an angle of $30 ^ { \circ }$ relative to level ground will clear a 10-foot wall 400 feet away.

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0°, 360°) rounded to the nearest tenth. - $\langle - 5,7 \rangle$

Use your grapher to determine which of the graphs matches the given polar equation. - $r = 4 \sin \theta$

Express the indicated roots of unity in standard form a + bi. -Tenth roots of unity

Express the indicated roots of unity in standard form a + bi. -Ninth roots of unity

Find a· b. - $a = 6 \mathbf { j } , \quad b = i + 5 j$

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°. - $( 4 \sqrt { 3 } , 12 )$

With your calculator set to radian mode and polar graphics capability, graph the following function in the window specified. - $\mathrm { r } = \cos \theta + \sin \theta , 0 \leq \theta \leq 2 \pi , [ - 2,2 ]$ by $[ - 2,2 ]$

Find the indicated roots. Write the answer in a + bi form. -Cube roots of $8 \mathrm { i }$

Plot the point with the given polar coordinates. - $\left( 2,0 ^ { \circ } \right)$ $Plot the point with the given polar coordinates. - \left( 2,0 ^ { \circ } \right)$

Solve the problem. -What is the minimum force required to prevent a ball weighing $16.6 \mathrm { lb }$ from rolling down a ramp which is inclined $28.6 ^ { \circ }$ with the horizontal?

Express the complex number in polar form. - $- 4$

Find a polar equation for the parametric equations. $x = f _ { 1 } ( \theta ) , y = f _ { 2 } ( \theta )$

Use the given graph to find the values of t that produce the graph in the given quadrant. - $x=3-|t|, y=t-2,-6 \leq t \leq 6$ $Use the given graph to find the values of t that produce the graph in the given quadrant. - x=3-|t|, y=t-2,-6 \leq t \leq 6 Quadrant I$ Quadrant I

Find an equivalent equation in polar coordinates. - $x ^ { 2 } + y ^ { 2 } = 100$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 6: Applications of Trigonometry

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi. - (1+i)20( 1 + i ) ^ { 20 }(1+i)20

Solve the problem. -One rope pulls a barge directly east with a force of 83 N, and another rope pulls the barge directly north with a force of 47 N. Find the magnitude of the resultant force acting on the barge.

Solve the problem. -Find the length of each petal of the polar curve r=8−3sin⁡4θr = 8 - 3 \sin 4 \thetar=8−3sin4θ . Note that this means the distance from the pole to the farthest point on the petal, not the arc length.

Find a polar equation for the parametric equations x=5cos⁡2θ,y=5cos⁡θsin⁡θx = 5 \cos ^ { 2 } \theta , y = 5 \cos \theta \sin \thetax=5cos2θ,y=5cosθsinθ

Solve the problem using a graphing calculator. -Determine whether a baseball hit 109 feet per second at an angle of 30∘30 ^ { \circ }30∘ relative to level ground will clear a 10-foot wall 400 feet away.

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0°, 360°) rounded to the nearest tenth. - ⟨−5,7⟩\langle - 5,7 \rangle⟨−5,7⟩

Use your grapher to determine which of the graphs matches the given polar equation. - r=4sin⁡θr = 4 \sin \thetar=4sinθ

Express the indicated roots of unity in standard form a + bi. -Tenth roots of unity

Express the indicated roots of unity in standard form a + bi. -Ninth roots of unity

Find a· b. - a=6j,b=i+5ja = 6 \mathbf { j } , \quad b = i + 5 ja=6j,b=i+5j

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°. - (43,12)( 4 \sqrt { 3 } , 12 )(43​,12)

Find the indicated roots. Write the answer in a + bi form. -Cube roots of 8i8 \mathrm { i }8i

Plot the point with the given polar coordinates. - (2,0∘)\left( 2,0 ^ { \circ } \right)(2,0∘)

Solve the problem. -What is the minimum force required to prevent a ball weighing 16.6lb16.6 \mathrm { lb }16.6lb from rolling down a ramp which is inclined 28.6∘28.6 ^ { \circ }28.6∘ with the horizontal?

Express the complex number in polar form. - −4- 4−4

Find a polar equation for the parametric equations. x=f1(θ),y=f2(θ)x = f _ { 1 } ( \theta ) , y = f _ { 2 } ( \theta )x=f1​(θ),y=f2​(θ)

Use the given graph to find the values of t that produce the graph in the given quadrant. - x=3−∣t∣,y=t−2,−6≤t≤6x=3-|t|, y=t-2,-6 \leq t \leq 6x=3−∣t∣,y=t−2,−6≤t≤6 Quadrant I

Find an equivalent equation in polar coordinates. - x2+y2=100x ^ { 2 } + y ^ { 2 } = 100x2+y2=100

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi. - $( 1 + i ) ^ { 20 }$

Solve the problem. -Find the length of each petal of the polar curve $r = 8 - 3 \sin 4 \theta$ . Note that this means the distance from the pole to the farthest point on the petal, not the arc length.

Find a polar equation for the parametric equations $x = 5 \cos ^ { 2 } \theta , y = 5 \cos \theta \sin \theta$

Solve the problem using a graphing calculator. -Determine whether a baseball hit 109 feet per second at an angle of $30 ^ { \circ }$ relative to level ground will clear a 10-foot wall 400 feet away.

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0°, 360°) rounded to the nearest tenth. - $\langle - 5,7 \rangle$

Use your grapher to determine which of the graphs matches the given polar equation. - $r = 4 \sin \theta$

Find a· b. - $a = 6 \mathbf { j } , \quad b = i + 5 j$

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°. - $( 4 \sqrt { 3 } , 12 )$

Find the indicated roots. Write the answer in a + bi form. -Cube roots of $8 \mathrm { i }$

Plot the point with the given polar coordinates. - $\left( 2,0 ^ { \circ } \right)$ $Plot the point with the given polar coordinates. - \left( 2,0 ^ { \circ } \right)$

Solve the problem. -What is the minimum force required to prevent a ball weighing $16.6 \mathrm { lb }$ from rolling down a ramp which is inclined $28.6 ^ { \circ }$ with the horizontal?

Express the complex number in polar form. - $- 4$

Find a polar equation for the parametric equations. $x = f _ { 1 } ( \theta ) , y = f _ { 2 } ( \theta )$

Use the given graph to find the values of t that produce the graph in the given quadrant. - $x=3-|t|, y=t-2,-6 \leq t \leq 6$ $Use the given graph to find the values of t that produce the graph in the given quadrant. - x=3-|t|, y=t-2,-6 \leq t \leq 6 Quadrant I$ Quadrant I

Find an equivalent equation in polar coordinates. - $x ^ { 2 } + y ^ { 2 } = 100$