Question 1

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations.
-$$x = - 3 t + 3 , y = 4 t - 6 ; t = - 4$$

Accepted Answer

A)  $( 9 , - 10 )$ 
B)  $( 0 , - 2 )$ 
C)  $( 15 , - 22 )$ 
D)  $( - 4 , - 6 )$ 
A)  $( 9 , - 10 )$ 
B)  $( 0 , - 2 )$ 
C)  $( 15 , - 22 )$ 
D)  $( - 4 , - 6 )$

Question 2

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { B } = 105.3 ^ { \circ } \
\mathrm { a } = 298 \mathrm {~cm} \
\mathrm {~b} = 1103 \mathrm {~cm}
\end{array}$$
If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$.

Accepted Answer

A)  $\mathrm { A } = 15.1 ^ { \circ } , \mathrm { C } = 59.6 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$ 
B)  $\mathrm { A } = 18.1 ^ { \circ } , \mathrm { C } = 56.6 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$ 
C)  no such triangle 
D)  $\mathrm { A } = 59.6 ^ { \circ } , \mathrm { C } = 15.1 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$ 
A)  $\mathrm { A } = 15.1 ^ { \circ } , \mathrm { C } = 59.6 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$ 
B)  $\mathrm { A } = 18.1 ^ { \circ } , \mathrm { C } = 56.6 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$ 
C)  no such triangle 
D)  $\mathrm { A } = 59.6 ^ { \circ } , \mathrm { C } = 15.1 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$

Question 3

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-$\frac { 50 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) } { 10 \left( \cos 32 ^ { \circ } + i \sin 32 ^ { \circ } \right) }$

Accepted Answer

A)  $- 2.3474 + 4.4147 \mathrm { i }$ 
B)  $4.4147 - 2.3474 \mathrm { i }$ 
C)  $- 49.0976 + 9.4565 \mathrm { i }$ 
D)  $9.4565 - 49.0976 \mathrm { i }$ 
A)  $- 2.3474 + 4.4147 \mathrm { i }$ 
B)  $4.4147 - 2.3474 \mathrm { i }$ 
C)  $- 49.0976 + 9.4565 \mathrm { i }$ 
D)  $9.4565 - 49.0976 \mathrm { i }$

Question 4

Write the complex number in trigonometric form $$r ( \cos \theta + i \sin \theta )$$ with θ in the interval [0°, 360°).
-$5 - 5 \sqrt { 3 } i$

Accepted Answer

A)  $10 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$ 
B)  $10 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right)$ 
C)  $5 \left( \cos 330 ^ { \circ } + \sin i 330 ^ { \circ } \right)$ 
D)  $5 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$ 
A)  $10 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$ 
B)  $10 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right)$ 
C)  $5 \left( \cos 330 ^ { \circ } + \sin i 330 ^ { \circ } \right)$ 
D)  $5 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$

Question 5

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$\frac { 15 \operatorname { cis } 156 ^ { \circ } } { 5 \operatorname { cis } 36 ^ { \circ } }$

Accepted Answer

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

Question 6

Draw a sketch to represent the vector. Refer to the vectors pictured here.  
-$c - d$

Accepted Answer

A)   
B)   
A)   
B)

Question 7

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations.
-$$\mathrm { x } = \mathrm { t } , \mathrm { y } = \mathrm { t } ^ { 3 } ; \mathrm { t } = - 2$$

Accepted Answer

A)  $( - 2,4 )$ 
B)  $( - 2 , - 8 )$ 
C)  $( - 8 , - 2 )$ 
D)  $( 2,8 )$ 
A)  $( - 2,4 )$ 
B)  $( - 2 , - 8 )$ 
C)  $( - 8 , - 2 )$ 
D)  $( 2,8 )$

Question 8

Find the angle between the pair of vectors to the nearest tenth of a degree.
-$$9 \mathbf { i } + 8 \mathbf { j } , - 3 \mathbf { i } + 6 \mathbf { j }$$

Accepted Answer

A)  $74.9 ^ { \circ }$ 
B)  $99.3 ^ { \circ }$ 
C)  $158.2 ^ { \circ }$ 
D)  $75.9 ^ { \circ }$ 
A)  $74.9 ^ { \circ }$ 
B)  $99.3 ^ { \circ }$ 
C)  $158.2 ^ { \circ }$ 
D)  $75.9 ^ { \circ }$

Question 9

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°.
-$( 0 , - \sqrt { 5 } )$

Accepted Answer

A)  $\left( \sqrt { 5 } , 0 ^ { \circ } \right) , \left( - \sqrt { 5 } , 180 ^ { \circ } \right)$ 
B)  $\left( \sqrt { 5 } , 270 ^ { \circ } \right) , \left( - \sqrt { 5 } , 90 ^ { \circ } \right)$ 
C)  $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 270 ^ { \circ } \right)$ 
D)  $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 0 ^ { \circ } \right)$ 
A)  $\left( \sqrt { 5 } , 0 ^ { \circ } \right) , \left( - \sqrt { 5 } , 180 ^ { \circ } \right)$ 
B)  $\left( \sqrt { 5 } , 270 ^ { \circ } \right) , \left( - \sqrt { 5 } , 90 ^ { \circ } \right)$ 
C)  $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 270 ^ { \circ } \right)$ 
D)  $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 0 ^ { \circ } \right)$

Question 10

For the given rectangular equation, give its equivalent polar equation.
-$$x ^ { 2 } + y ^ { 2 } = 100$$

Accepted Answer

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

Question 11

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { A } = 44.29 ^ { \circ } \
\mathrm { a } = 51.82 \mathrm { yd } \
\mathrm { b } = 63.64 \mathrm { yd }
\end{array}$$
If necessary, round angles and side lengths to the nearest hundredth.

Accepted Answer

A)  no such triangle 
B)  $\mathrm { B } _ { 1 } = 59.04 ^ { \circ } , \mathrm { C } _ { 1 } = 76.67 ^ { \circ } , \mathrm { c } _ { 1 } = 72.21 \mathrm { yd }$ $\mathrm { B } _ { 2 } = 120.96 ^ { \circ } , \mathrm { C } _ { 2 } = 14.75 ^ { \circ } , \mathrm { c } _ { 2 } = 18.89 \mathrm { yd }$ 
C)  $\mathrm { B } _ { 1 } = 76.67 ^ { \circ } , \mathrm { C } _ { 1 } = 59.04 ^ { \circ } , \mathrm { c } _ { 1 } = 72.21 \mathrm { yd }$ 
D)  $\mathrm { B } = 59.04 ^ { \circ } , \mathrm { C } = 76.67 ^ { \circ } , \mathrm { c } = 72.21 \mathrm { yd }$ $\mathrm { B } _ { 2 } = 14.75 ^ { \circ } , \mathrm { C } _ { 2 } = 120.96 ^ { \circ } , \mathrm { c } _ { 2 } = 18.89 \mathrm { yd }$ 
A)  no such triangle 
B)  $\mathrm { B } _ { 1 } = 59.04 ^ { \circ } , \mathrm { C } _ { 1 } = 76.67 ^ { \circ } , \mathrm { c } _ { 1 } = 72.21 \mathrm { yd }$ $\mathrm { B } _ { 2 } = 120.96 ^ { \circ } , \mathrm { C } _ { 2 } = 14.75 ^ { \circ } , \mathrm { c } _ { 2 } = 18.89 \mathrm { yd }$ 
C)  $\mathrm { B } _ { 1 } = 76.67 ^ { \circ } , \mathrm { C } _ { 1 } = 59.04 ^ { \circ } , \mathrm { c } _ { 1 } = 72.21 \mathrm { yd }$ 
D)  $\mathrm { B } = 59.04 ^ { \circ } , \mathrm { C } = 76.67 ^ { \circ } , \mathrm { c } = 72.21 \mathrm { yd }$ $\mathrm { B } _ { 2 } = 14.75 ^ { \circ } , \mathrm { C } _ { 2 } = 120.96 ^ { \circ } , \mathrm { c } _ { 2 } = 18.89 \mathrm { yd }$

Question 12

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to one decimal place.
-

Accepted Answer

A)  $132.7 \mathrm { lb }$ 
B)  $21,459.5 \mathrm { lb }$ 
C)  $180.3 \mathrm { lb }$ 
D)  $146.5 \mathrm { lb }$ 
A)  $132.7 \mathrm { lb }$ 
B)  $21,459.5 \mathrm { lb }$ 
C)  $180.3 \mathrm { lb }$ 
D)  $146.5 \mathrm { lb }$

Question 13

Find sum of the pair of complex numbers.
-$$- 5 + 5 i , - 9$$

Accepted Answer

A)  $- 5 + 14 i$ 
B)  $- 9$ 
C)  $- 5 - 4 \mathrm { i }$ 
D)  $- 14 + 5 i$ 
A)  $- 5 + 14 i$ 
B)  $- 9$ 
C)  $- 5 - 4 \mathrm { i }$ 
D)  $- 14 + 5 i$

Question 14

Solve the problem.
-A ship leaves point $A$ and travels directly north to point $B$. From point $B$, the ship then travels due east to point $C$. The magnitude of the vector from point $A$ to point $C$ is 134 . Find the magnitude of the northern vector. Find the magnitude of the eastern vector.

Accepted Answer

A)  $67 \sqrt { 2 }$ north; $67 \sqrt { 2 }$ east 
B)  67 north; $67 \sqrt { 3 }$ east 
C)  67 north; 67 east 
D)  $67 \sqrt { 3 }$ north; 67 east 
A)  $67 \sqrt { 2 }$ north; $67 \sqrt { 2 }$ east 
B)  67 north; $67 \sqrt { 3 }$ east 
C)  67 north; 67 east 
D)  $67 \sqrt { 3 }$ north; 67 east

Question 15

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°.
-$$( - \sqrt { 3 } , - \sqrt { 3 } )$$

Accepted Answer

A)  $\left( \sqrt { 6 } , 315 ^ { \circ } \right)$ 
B)  $\left( \sqrt { 6 } , 225 ^ { \circ } \right)$ 
C)  $\left( 6,225 ^ { \circ } \right)$ 
D)  $\left( \sqrt { 3 } , 135 ^ { \circ } \right)$ 
A)  $\left( \sqrt { 6 } , 315 ^ { \circ } \right)$ 
B)  $\left( \sqrt { 6 } , 225 ^ { \circ } \right)$ 
C)  $\left( 6,225 ^ { \circ } \right)$ 
D)  $\left( \sqrt { 3 } , 135 ^ { \circ } \right)$

Question 16

Graph the polar equation for θ in [0°, 360°).
-$$r = 3 ( 2 + 2 \sin \theta )$$

Accepted Answer

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

Question 17

Plot the point.
-$$\left( 4 , - 225 ^ { \circ } \right)$$

Accepted Answer

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

Question 18

Find an equivalent equation in rectangular coordinates.
-$$\mathbf { r } = \cos \theta$$

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = x$ 
B)  $( x + y ) ^ { 2 } = y$ 
C)  $( x + y ) ^ { 2 } = x$ 
D)  $x ^ { 2 } + y ^ { 2 } = y$ 
A)  $x ^ { 2 } + y ^ { 2 } = x$ 
B)  $( x + y ) ^ { 2 } = y$ 
C)  $( x + y ) ^ { 2 } = x$ 
D)  $x ^ { 2 } + y ^ { 2 } = y$

Question 19

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 1 } { - 6 - 8 i }$$

Accepted Answer

A)  $- \frac { 3 } { 50 } - \frac { 2 } { 25 } \mathrm { i }$ 
B)  $\frac { 3 } { 14 } - \frac { 2 } { 7 } i$ 
C)  $\frac { 3 } { 14 } + \frac { 2 } { 7 } \mathrm { i }$ 
D)  $- \frac { 3 } { 50 } + \frac { 2 } { 25 } \mathrm { i }$ 
A)  $- \frac { 3 } { 50 } - \frac { 2 } { 25 } \mathrm { i }$ 
B)  $\frac { 3 } { 14 } - \frac { 2 } { 7 } i$ 
C)  $\frac { 3 } { 14 } + \frac { 2 } { 7 } \mathrm { i }$ 
D)  $- \frac { 3 } { 50 } + \frac { 2 } { 25 } \mathrm { i }$

Question 20

Graph the complex number.
-$$6 + 2 i \sqrt { 5 }$$

Accepted Answer

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

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = - 3 t + 3 , y = 4 t - 6 ; t = - 4$

Find the missing parts of the triangle. - =105. =298 =1103 If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$ .

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. - $\frac { 50 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) } { 10 \left( \cos 32 ^ { \circ } + i \sin 32 ^ { \circ } \right) }$

Write the complex number in trigonometric form $r ( \cos \theta + i \sin \theta )$ with θ in the interval [0°, 360°). - $5 - 5 \sqrt { 3 } i$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 15 \operatorname { cis } 156 ^ { \circ } } { 5 \operatorname { cis } 36 ^ { \circ } }$

Draw a sketch to represent the vector. Refer to the vectors pictured here. - $c - d$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $\mathrm { x } = \mathrm { t } , \mathrm { y } = \mathrm { t } ^ { 3 } ; \mathrm { t } = - 2$

Find the angle between the pair of vectors to the nearest tenth of a degree. - $9 \mathbf { i } + 8 \mathbf { j } , - 3 \mathbf { i } + 6 \mathbf { j }$

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( 0 , - \sqrt { 5 } )$

For the given rectangular equation, give its equivalent polar equation. - $x ^ { 2 } + y ^ { 2 } = 100$

Find the missing parts of the triangle. - =44.2 =51.82 =63.64 If necessary, round angles and side lengths to the nearest hundredth.

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to one decimal place. -

Find sum of the pair of complex numbers. - $- 5 + 5 i , - 9$

Solve the problem. -A ship leaves point $A$ and travels directly north to point $B$ . From point $B$ , the ship then travels due east to point $C$ . The magnitude of the vector from point $A$ to point $C$ is 134 . Find the magnitude of the northern vector. Find the magnitude of the eastern vector.

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°. - $( - \sqrt { 3 } , - \sqrt { 3 } )$

Graph the polar equation for θ in [0°, 360°). - $r = 3 ( 2 + 2 \sin \theta )$ $Graph the polar equation for θ in [0°, 360°). - r = 3 ( 2 + 2 \sin \theta )$

Plot the point. - $\left( 4 , - 225 ^ { \circ } \right)$ $Plot the point. - \left( 4 , - 225 ^ { \circ } \right)$

Find an equivalent equation in rectangular coordinates. - $\mathbf { r } = \cos \theta$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 1 } { - 6 - 8 i }$

Graph the complex number. - $6 + 2 i \sqrt { 5 }$ $Graph the complex number. - 6 + 2 i \sqrt { 5 }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 8: Applications of Trigonometry

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - x=−3t+3,y=4t−6;t=−4x = - 3 t + 3 , y = 4 t - 6 ; t = - 4x=−3t+3,y=4t−6;t=−4

Find the missing parts of the triangle. - =105. =298 =1103 If necessary, round angles the nearest tenth and side lengths to the nearest cm\mathrm { cm }cm .

Write the complex number in trigonometric form r(cos⁡θ+isin⁡θ)r ( \cos \theta + i \sin \theta )r(cosθ+isinθ) with θ in the interval [0°, 360°). - 5−53i5 - 5 \sqrt { 3 } i5−53​i

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - 15cis⁡156∘5cis⁡36∘\frac { 15 \operatorname { cis } 156 ^ { \circ } } { 5 \operatorname { cis } 36 ^ { \circ } }5cis36∘15cis156∘​

Draw a sketch to represent the vector. Refer to the vectors pictured here. - c−dc - dc−d

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - x=t,y=t3;t=−2\mathrm { x } = \mathrm { t } , \mathrm { y } = \mathrm { t } ^ { 3 } ; \mathrm { t } = - 2x=t,y=t3;t=−2

Find the angle between the pair of vectors to the nearest tenth of a degree. - 9i+8j,−3i+6j9 \mathbf { i } + 8 \mathbf { j } , - 3 \mathbf { i } + 6 \mathbf { j }9i+8j,−3i+6j

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - (0,−5)( 0 , - \sqrt { 5 } )(0,−5​)

For the given rectangular equation, give its equivalent polar equation. - x2+y2=100x ^ { 2 } + y ^ { 2 } = 100x2+y2=100

Find the missing parts of the triangle. - =44.2 =51.82 =63.64 If necessary, round angles and side lengths to the nearest hundredth.

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to one decimal place. -

Find sum of the pair of complex numbers. - −5+5i,−9- 5 + 5 i , - 9−5+5i,−9

Solve the problem. -A ship leaves point AAA and travels directly north to point BBB . From point BBB , the ship then travels due east to point CCC . The magnitude of the vector from point AAA to point CCC is 134 . Find the magnitude of the northern vector. Find the magnitude of the eastern vector.

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°. - (−3,−3)( - \sqrt { 3 } , - \sqrt { 3 } )(−3​,−3​)

Graph the polar equation for θ in [0°, 360°). - r=3(2+2sin⁡θ)r = 3 ( 2 + 2 \sin \theta )r=3(2+2sinθ)

Plot the point. - (4,−225∘)\left( 4 , - 225 ^ { \circ } \right)(4,−225∘)

Find an equivalent equation in rectangular coordinates. - r=cos⁡θ\mathbf { r } = \cos \thetar=cosθ

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - 1−6−8i\frac { 1 } { - 6 - 8 i }−6−8i1​

Graph the complex number. - 6+2i56 + 2 i \sqrt { 5 }6+2i5​

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = - 3 t + 3 , y = 4 t - 6 ; t = - 4$

Find the missing parts of the triangle. - =105. =298 =1103 If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$ .

Write the complex number in trigonometric form $r ( \cos \theta + i \sin \theta )$ with θ in the interval [0°, 360°). - $5 - 5 \sqrt { 3 } i$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 15 \operatorname { cis } 156 ^ { \circ } } { 5 \operatorname { cis } 36 ^ { \circ } }$

Draw a sketch to represent the vector. Refer to the vectors pictured here. - $c - d$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $\mathrm { x } = \mathrm { t } , \mathrm { y } = \mathrm { t } ^ { 3 } ; \mathrm { t } = - 2$

Find the angle between the pair of vectors to the nearest tenth of a degree. - $9 \mathbf { i } + 8 \mathbf { j } , - 3 \mathbf { i } + 6 \mathbf { j }$

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( 0 , - \sqrt { 5 } )$

For the given rectangular equation, give its equivalent polar equation. - $x ^ { 2 } + y ^ { 2 } = 100$

Find sum of the pair of complex numbers. - $- 5 + 5 i , - 9$

Solve the problem. -A ship leaves point $A$ and travels directly north to point $B$ . From point $B$ , the ship then travels due east to point $C$ . The magnitude of the vector from point $A$ to point $C$ is 134 . Find the magnitude of the northern vector. Find the magnitude of the eastern vector.

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°. - $( - \sqrt { 3 } , - \sqrt { 3 } )$

Graph the polar equation for θ in [0°, 360°). - $r = 3 ( 2 + 2 \sin \theta )$ $Graph the polar equation for θ in [0°, 360°). - r = 3 ( 2 + 2 \sin \theta )$

Plot the point. - $\left( 4 , - 225 ^ { \circ } \right)$ $Plot the point. - \left( 4 , - 225 ^ { \circ } \right)$

Find an equivalent equation in rectangular coordinates. - $\mathbf { r } = \cos \theta$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 1 } { - 6 - 8 i }$

Graph the complex number. - $6 + 2 i \sqrt { 5 }$ $Graph the complex number. - 6 + 2 i \sqrt { 5 }$