Question 1

The graph of a polar equation is given. Select the polar equation for the graph.
-

Accepted Answer

A)  $r \sin \theta = 2$ 
B)  $r = 4 \cos \theta$ 
C)  $r = 4 \sin \theta$ 
D)  $\mathrm { r } = 2$ 
A)  $r \sin \theta = 2$ 
B)  $r = 4 \cos \theta$ 
C)  $r = 4 \sin \theta$ 
D)  $\mathrm { r } = 2$

Question 2

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
-

Accepted Answer

A)  $\mathrm { B } = 37.2 ^ { \circ } , \mathrm { b } = 26.8 \mathrm { ft } , \mathrm { c } = 21.8 \mathrm { ft }$ 
B)  $B = 36.8 ^ { \circ } , \mathrm { b } = 257.5 \mathrm { ft } , \mathrm { c } = 321.5 \mathrm { ft }$ 
C)  $\mathrm { B } = 37.2 ^ { \circ } , \mathrm { b } = 259.9 \mathrm { ft } , \mathrm { c } = 321.5 \mathrm { ft }$ 
D)  $\mathrm { B } = 37.2 ^ { \circ } , \mathrm { b } = 321.5 \mathrm { ft } , \mathrm { c } = 259.9 \mathrm { ft }$ 
A)  $\mathrm { B } = 37.2 ^ { \circ } , \mathrm { b } = 26.8 \mathrm { ft } , \mathrm { c } = 21.8 \mathrm { ft }$ 
B)  $B = 36.8 ^ { \circ } , \mathrm { b } = 257.5 \mathrm { ft } , \mathrm { c } = 321.5 \mathrm { ft }$ 
C)  $\mathrm { B } = 37.2 ^ { \circ } , \mathrm { b } = 259.9 \mathrm { ft } , \mathrm { c } = 321.5 \mathrm { ft }$ 
D)  $\mathrm { B } = 37.2 ^ { \circ } , \mathrm { b } = 321.5 \mathrm { ft } , \mathrm { c } = 259.9 \mathrm { ft }$

Question 3

Determine the number of triangles ABC possible with the given parts.
-$$a = 35 , b = 46 , A = 21 ^ { \circ }$$

Accepted Answer

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

Question 4

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.
-A fishing boat leaves port on a bearing of $39 ^ { \circ }$ and travels $11.8 \mathrm { mi }$. The boat then turns due east and travels $2.9 \mathrm { mi }$. How far is the fishing boat from port, and what is its bearing from port?

Accepted Answer

A)  $9.7 \mathrm { mi } ; 9.4 ^ { \circ }$ 
B)  $13.8 \mathrm { mi }$; $9.4 ^ { \circ }$ 
C)  $13.8 \mathrm { mi } ; 48.4 ^ { \circ }$ 
D)  $10.2 \mathrm { mi } ; 48.4 ^ { \circ }$ 
A)  $9.7 \mathrm { mi } ; 9.4 ^ { \circ }$ 
B)  $13.8 \mathrm { mi }$; $9.4 ^ { \circ }$ 
C)  $13.8 \mathrm { mi } ; 48.4 ^ { \circ }$ 
D)  $10.2 \mathrm { mi } ; 48.4 ^ { \circ }$

Question 5

Plot the point.
-$\left(-4, \frac{-3 \pi}{4}\right)$

Accepted Answer

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

Question 6

The rectangular coordinates of a point are given. Express the point in polar coordinates with $$r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$$
-$( - 2,0 )$

Accepted Answer

A)  $\left( 2,270 ^ { \circ } \right)$ 
B)  $\left( 2,90 ^ { \circ } \right)$ 
C)  $\left( 2,180 ^ { \circ } \right)$ 
D)  $\left( - 2,180 ^ { \circ } \right)$ 
A)  $\left( 2,270 ^ { \circ } \right)$ 
B)  $\left( 2,90 ^ { \circ } \right)$ 
C)  $\left( 2,180 ^ { \circ } \right)$ 
D)  $\left( - 2,180 ^ { \circ } \right)$

Question 7

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in $$\left[ 0,360 ^ { \circ } \right]$$
-$$\langle 2 \sqrt { 2 } , - 2 \sqrt { 2 } \rangle$$

Accepted Answer

A)  $4 ; 315 ^ { \circ }$ 
B)  $4 \sqrt { 2 } ; 45 ^ { \circ }$ 
C)  $4 ; 135 ^ { \circ }$ 
D)  $8 ; 315 ^ { \circ }$ 
A)  $4 ; 315 ^ { \circ }$ 
B)  $4 \sqrt { 2 } ; 45 ^ { \circ }$ 
C)  $4 ; 135 ^ { \circ }$ 
D)  $8 ; 315 ^ { \circ }$

Question 8

Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 4 } + 16 = 0$$

Accepted Answer

A)  $\left\{ \sqrt { 2 } \operatorname { cis } 45 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 315 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 135 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 225 ^ { \circ } \right\}$ 
B)  $\left\{ \sqrt { 3 } \operatorname { cis } 26.565 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 333.435 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 153.435 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 206.565 ^ { \circ } \right\}$ 
C)  $\left\{ 16 \right.$ cis $45 ^ { \circ } , 16$ cis $315 ^ { \circ } , 16$ cis $135 ^ { \circ } , 16$ cis $\left. 225 ^ { \circ } \right\}$ 
D)  $\left\{ 2 \operatorname { cis } 45 ^ { \circ } , 2 \operatorname { cis } 315 ^ { \circ } , 2 \operatorname { cis } 135 ^ { \circ } , 2 \operatorname { cis } 225 ^ { \circ } \right\}$ 
A)  $\left\{ \sqrt { 2 } \operatorname { cis } 45 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 315 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 135 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 225 ^ { \circ } \right\}$ 
B)  $\left\{ \sqrt { 3 } \operatorname { cis } 26.565 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 333.435 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 153.435 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 206.565 ^ { \circ } \right\}$ 
C)  $\left\{ 16 \right.$ cis $45 ^ { \circ } , 16$ cis $315 ^ { \circ } , 16$ cis $135 ^ { \circ } , 16$ cis $\left. 225 ^ { \circ } \right\}$ 
D)  $\left\{ 2 \operatorname { cis } 45 ^ { \circ } , 2 \operatorname { cis } 315 ^ { \circ } , 2 \operatorname { cis } 135 ^ { \circ } , 2 \operatorname { cis } 225 ^ { \circ } \right\}$

Question 9

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $$0 \leq \theta < 2 \pi$$
-$$r = \frac { a \left( 1 - e ^ { 2 } \right) } { 1 + e \cos \theta }$$ Given that the polar equation r models the orbits of the planets, estimate the closest approach of Pluto's orbit, for which a = 39.4 and e = 0.249, to the sun.

Accepted Answer

A)  About 39 astronomical units 
B)  About 74 astronomical units 
C)  About 30 astronomical units 
D)  About 50 astronomical units 
A)  About 39 astronomical units 
B)  About 74 astronomical units 
C)  About 30 astronomical units 
D)  About 50 astronomical units

Question 10

Solve the problem.
-If u =-5, 3 , v =-2, -6 , and w =-3, 12, evaluate (u + v) ·w.

Accepted Answer

A)  -10 
B)  -19 
C)  -8 
D)  -15 
A)  -10 
B)  -19 
C)  -8 
D)  -15

Question 11

Use the figure to find the specified vector.
-Find $\mathbf { a } + \mathbf { b }$

Accepted Answer

A)  $\langle 11,11 \rangle$ 
B)  $\langle - 5,3 \rangle$ 
C)  $\langle 5,11 \rangle$ 
D)  $\langle - 5,11 \rangle$ 
A)  $\langle 11,11 \rangle$ 
B)  $\langle - 5,3 \rangle$ 
C)  $\langle 5,11 \rangle$ 
D)  $\langle - 5,11 \rangle$

Question 12

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $$0 \leq \theta < 2 \pi$$
-$r = 4 \cos \theta , r = - 1 + 2 \cos \theta$

Accepted Answer

A)  $\left( 2 , \frac { 2 \pi } { 3 } \right) , \left( - 2 , \frac { 4 \pi } { 3 } \right)$ 
B)  $\left( 2 , \frac { 5 \pi } { 6 } \right) , \left( 2 , \frac { \pi } { 6 } \right)$ 
C)  $\left\{ 2 , \frac { 2 \pi } { 3 } \right) , \left( 2 , \frac { 4 \pi } { 3 } \right)$ 
D)  $\left\{ - 2 , \frac { 5 \pi } { 3 } \right) , \left( - 2 , \frac { \pi } { 3 } \right)$ 
A)  $\left( 2 , \frac { 2 \pi } { 3 } \right) , \left( - 2 , \frac { 4 \pi } { 3 } \right)$ 
B)  $\left( 2 , \frac { 5 \pi } { 6 } \right) , \left( 2 , \frac { \pi } { 6 } \right)$ 
C)  $\left\{ 2 , \frac { 2 \pi } { 3 } \right) , \left( 2 , \frac { 4 \pi } { 3 } \right)$ 
D)  $\left\{ - 2 , \frac { 5 \pi } { 3 } \right) , \left( - 2 , \frac { \pi } { 3 } \right)$

Question 13

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation
for the curve.
-$x=t^{2}, y=\sqrt{t}+3, \text { for } t \text { in }[0,4]$

Accepted Answer

A) 
 
$y = \sqrt { x } + 0$, for $x$ in $[ 0,16 ]$ 
B) 
 
$y = x ^ { 2 } + 0$, for $x$ in $[ 0,2 ]$ 
C) 
 
$$y = \frac { 1 } { 8 } x + 0 , \text { for } x \text { in } [ 0,16 ]$$ 
D)

$$y = \sqrt [ 4 ] { x } + 3 , \text { for } x \text { in } [ 0,16 ]$$ 
A) 
 
$y = \sqrt { x } + 0$, for $x$ in $[ 0,16 ]$ 
B) 
 
$y = x ^ { 2 } + 0$, for $x$ in $[ 0,2 ]$ 
C) 
 
$$y = \frac { 1 } { 8 } x + 0 , \text { for } x \text { in } [ 0,16 ]$$ 
D)

$$y = \sqrt [ 4 ] { x } + 3 , \text { for } x \text { in } [ 0,16 ]$$

Question 14

Provide an appropriate response.
-State the formulas for the area of a triangle ABC that were derived using the law of sines.

Accepted Answer

The answer of Provide an appropriate response.
-State the formulas for...

Question 15

Find the component form of the indicated vector.
-Let $\mathbf { u } = \langle - 8,7 \rangle$. Find $- 6 \mathbf { u }$.

Accepted Answer

A)  $\langle 48,42 \rangle$ 
B)  $\langle - 48,42 \rangle$ 
C)  $\langle 48 , - 42 \rangle$ 
D)  $\langle - 48 , - 42 \rangle$ 
A)  $\langle 48,42 \rangle$ 
B)  $\langle - 48,42 \rangle$ 
C)  $\langle 48 , - 42 \rangle$ 
D)  $\langle - 48 , - 42 \rangle$

Question 16

Plot the point.
-$$\left( - 2 , \frac { 3 \pi } { 4 } \right)$$

Accepted Answer

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

Question 17

Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 3 } + 8 = 0$$

Accepted Answer

A)  $\left\{ 2 \operatorname { cis } 180 ^ { \circ } , 2 \operatorname { cis } 120 ^ { \circ } , 2 \operatorname { cis } 240 ^ { \circ } \right\}$ 
B)  $\left\{ 2 \operatorname { cis } 180 ^ { \circ } , 2 \operatorname { cis } 240 ^ { \circ } , 2 \operatorname { cis } 240 ^ { \circ } \right\}$ 
C)  $\left\{ 2 \operatorname { cis } 180 ^ { \circ } , 2 \operatorname { cis } 120 ^ { \circ } , 2 \operatorname { cis } 300 ^ { \circ } \right\}$ 
D)  $\left\{ 2 \operatorname { cis } 180 ^ { \circ } , 2 \operatorname { cis } 60 ^ { \circ } , 2 \operatorname { cis } 300 ^ { \circ } \right\}$ 
A)  $\left\{ 2 \operatorname { cis } 180 ^ { \circ } , 2 \operatorname { cis } 120 ^ { \circ } , 2 \operatorname { cis } 240 ^ { \circ } \right\}$ 
B)  $\left\{ 2 \operatorname { cis } 180 ^ { \circ } , 2 \operatorname { cis } 240 ^ { \circ } , 2 \operatorname { cis } 240 ^ { \circ } \right\}$ 
C)  $\left\{ 2 \operatorname { cis } 180 ^ { \circ } , 2 \operatorname { cis } 120 ^ { \circ } , 2 \operatorname { cis } 300 ^ { \circ } \right\}$ 
D)  $\left\{ 2 \operatorname { cis } 180 ^ { \circ } , 2 \operatorname { cis } 60 ^ { \circ } , 2 \operatorname { cis } 300 ^ { \circ } \right\}$

Question 18

Find sum of the pair of complex numbers.
-9i, -3

Accepted Answer

A)  9 - 3i 
B)  -3 - 9i 
C)  6i 
D)  -3 + 9i 
A)  9 - 3i 
B)  -3 - 9i 
C)  6i 
D)  -3 + 9i

Question 19

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

Accepted Answer

A) 
  
B)  $\longrightarrow$ 
A) 
  
B)  $\longrightarrow$

Question 20

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 3 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) } { 4 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right) }$$

Accepted Answer

A)  $\frac { 3 } { 8 } - \frac { 3 } { 8 } \mathrm { i } \sqrt { 3 }$ 
B)  $\frac { 3 } { 4 } \sqrt { 3 } - \frac { 3 } { 8 } \mathrm { i }$ 
C)  $\frac { 3 } { 8 } + \frac { 3 } { 8 } i \sqrt { 3 }$ 
D)  $\frac { 3 } { 4 } \sqrt { 3 } + \frac { 3 } { 8 } \mathrm { i }$ 
A)  $\frac { 3 } { 8 } - \frac { 3 } { 8 } \mathrm { i } \sqrt { 3 }$ 
B)  $\frac { 3 } { 4 } \sqrt { 3 } - \frac { 3 } { 8 } \mathrm { i }$ 
C)  $\frac { 3 } { 8 } + \frac { 3 } { 8 } i \sqrt { 3 }$ 
D)  $\frac { 3 } { 4 } \sqrt { 3 } + \frac { 3 } { 8 } \mathrm { i }$

The graph of a polar equation is given. Select the polar equation for the graph. -

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. -

Determine the number of triangles ABC possible with the given parts. - $a = 35 , b = 46 , A = 21 ^ { \circ }$

Plot the point. - $\left(-4, \frac{-3 \pi}{4}\right)$ $Plot the point. - \left(-4, \frac{-3 \pi}{4}\right)$

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $( - 2,0 )$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle 2 \sqrt { 2 } , - 2 \sqrt { 2 } \rangle$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 4 } + 16 = 0$

Solve the problem. -If u =-5, 3 , v =-2, -6 , and w =-3, 12, evaluate (u + v) ·w.

Use the figure to find the specified vector. -Find $\mathbf { a } + \mathbf { b }$ $Use the figure to find the specified vector. -Find \mathbf { a } + \mathbf { b }$

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $0 \leq \theta < 2 \pi$ - $r = 4 \cos \theta , r = - 1 + 2 \cos \theta$

Provide an appropriate response. -State the formulas for the area of a triangle ABC that were derived using the law of sines.

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 8,7 \rangle$ . Find $- 6 \mathbf { u }$ .

Plot the point. - $\left( - 2 , \frac { 3 \pi } { 4 } \right)$ $Plot the point. - \left( - 2 , \frac { 3 \pi } { 4 } \right)$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 3 } + 8 = 0$

Find sum of the pair of complex numbers. -9i, -3

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

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 3 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) } { 4 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right) }$

Review of Basic Concepts

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

Filters

Exam 9: Applications of Trigonometry