Question 1

Find the given power. Write answer in rectangular form.
-$$( 1 + i ) ^ { 20 }$$

Accepted Answer

A)  1024 
B)  1024i 
C)  -1024i 
D)  -1024 
A)  1024 
B)  1024i 
C)  -1024i 
D)  -1024

Question 2

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation
for the curve.
-$x=5 \tan t, y=4 \sec t \text {, for } t \text { in }[0,2 \pi]$

Accepted Answer

A) 
 
$$\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 25 } = 1 , \text { for } x \text { in } ( - \infty , \infty )$$ 
B) 
 
$$y = 4 \sqrt { 1 + \frac { x ^ { 2 } } { 25 } } , \text { for } x \text { in } ( - \infty , \infty )$$ 
C) 
 
$$\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 25 } = 1 , \text { for } x \text { in } ( - \infty , \infty )$$ 
D) 
 
$$y = x ^ { 2 } - 9 , \text { for } x \text { in } [ - 3,3 ]$$ 
A) 
 
$$\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 25 } = 1 , \text { for } x \text { in } ( - \infty , \infty )$$ 
B) 
 
$$y = 4 \sqrt { 1 + \frac { x ^ { 2 } } { 25 } } , \text { for } x \text { in } ( - \infty , \infty )$$ 
C) 
 
$$\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 25 } = 1 , \text { for } x \text { in } ( - \infty , \infty )$$ 
D) 
 
$$y = x ^ { 2 } - 9 , \text { for } x \text { in } [ - 3,3 ]$$

Question 3

Find the given power. Write answer in rectangular form.
-$$( 1 - i ) ^ { 10 }$$

Accepted Answer

A)  $- 32 + 32 i$ 
B)  32 
C)  $- 32 \mathrm { i }$ 
D)  $32 - 32 i$ 
A)  $- 32 + 32 i$ 
B)  32 
C)  $- 32 \mathrm { i }$ 
D)  $32 - 32 i$

Question 4

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-Tia is going to stain her triangular concrete patio. The patio is approximately 14 feet by 18 feet by 10 feet. If one can of stain covers $12 \mathrm { ft } ^ { 2 }$, how many cans of stain will she need?

Accepted Answer

A)  6 cans 
B)  79 cans 
C)  2 cans 
D)  105 cans 
A)  6 cans 
B)  79 cans 
C)  2 cans 
D)  105 cans

Question 5

Find an equivalent equation in rectangular coordinates.
-$$r = \frac { 5 } { 1 + \cos \theta }$$

Accepted Answer

A)  $y ^ { 2 } = 10 x - 25$ 
B)  $x ^ { 2 } = 25 - 10 y$ 
C)  $x ^ { 2 } = 10 y - 25$ 
D)  $y ^ { 2 } = 25 - 10 x$ 
A)  $y ^ { 2 } = 10 x - 25$ 
B)  $x ^ { 2 } = 25 - 10 y$ 
C)  $x ^ { 2 } = 10 y - 25$ 
D)  $y ^ { 2 } = 25 - 10 x$

Question 6

Solve the problem.
-A painter is going to apply a special coating to a triangular metal plate on a new building. Two sides measure are $10.0 \mathrm {~m}$ and $7.1 \mathrm {~m}$. She knows that the angle between these sides is $37.2 ^ { \circ }$. What is the area of the surface she plans to cover with the coating? Round to the nearest square meter.

Accepted Answer

A)  $19 \mathrm {~m} ^ { 2 }$ 
B)  $30 \mathrm {~m} ^ { 2 }$ 
C)  $28 m ^ { 2 }$ 
D)  $21 \mathrm {~m} ^ { 2 }$ 
A)  $19 \mathrm {~m} ^ { 2 }$ 
B)  $30 \mathrm {~m} ^ { 2 }$ 
C)  $28 m ^ { 2 }$ 
D)  $21 \mathrm {~m} ^ { 2 }$

Question 7

Find the indicated vector.
-Let $\mathbf { u } = \langle 5,3 \rangle$. Find $- 2 \mathbf { u }$.

Accepted Answer

A)  $\langle 10,6 \rangle$ 
B)  $\langle - 10,6 \rangle$ 
C)  $\langle - 10 , - 6 \rangle$ 
D)  $\langle 10 , - 6 \rangle$ 
A)  $\langle 10,6 \rangle$ 
B)  $\langle - 10,6 \rangle$ 
C)  $\langle - 10 , - 6 \rangle$ 
D)  $\langle 10 , - 6 \rangle$

Question 8

Find the given power. Write answer in rectangular form.
-$( - \mathrm { i } ) ^ { 11 }$

Accepted Answer

A)  $- 1$ 
B)  $\mathrm { i }$ 
C)  1 
D)  $- \mathrm { i }$ 
A)  $- 1$ 
B)  $\mathrm { i }$ 
C)  1 
D)  $- \mathrm { i }$

Question 9

Find the missing parts of the triangle.
-$$\begin{array} { l } 
B = 15.6 ^ { \circ } \
b = 16.58 \
a = 30.83
\end{array}$$
If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.

Accepted Answer

A)  $\mathrm { A } _ { 1 } = 30 ^ { \circ } , \mathrm { C } _ { 1 } = 134.4 ^ { \circ } , \mathrm { c } _ { 1 } = 44.05$; 
B)  $\mathrm { A } = 150 ^ { \circ } , \mathrm { C } = 14.4 ^ { \circ } , \mathrm { c } = 15.33$
$$\mathrm { A } _ { 2 } = 150 ^ { \circ } , \mathrm { C } _ { 2 } = 14.4 ^ { \circ } , \mathrm { c } _ { 2 } = 15.33$$ 
C)  $\mathrm { A } = 30 ^ { \circ } , \mathrm { C } = 134.4 ^ { \circ } , \mathrm { c } = 44.05$ 
D)  no such triangle 
A)  $\mathrm { A } _ { 1 } = 30 ^ { \circ } , \mathrm { C } _ { 1 } = 134.4 ^ { \circ } , \mathrm { c } _ { 1 } = 44.05$; 
B)  $\mathrm { A } = 150 ^ { \circ } , \mathrm { C } = 14.4 ^ { \circ } , \mathrm { c } = 15.33$
$$\mathrm { A } _ { 2 } = 150 ^ { \circ } , \mathrm { C } _ { 2 } = 14.4 ^ { \circ } , \mathrm { c } _ { 2 } = 15.33$$ 
C)  $\mathrm { A } = 30 ^ { \circ } , \mathrm { C } = 134.4 ^ { \circ } , \mathrm { c } = 44.05$ 
D)  no such triangle

Question 10

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-$$\frac { 60 \left( \cos 150 ^ { \circ } + \mathrm { i } \sin 150 ^ { \circ } \right) } { 10 \left( \cos 39 ^ { \circ } + \mathrm { i } \sin 39 ^ { \circ } \right) }$$

Accepted Answer

A)  $- 51.8731 - 30.1527 \mathrm { i }$ 
B)  $- 2.1502 + 5.6015 \mathrm { i }$ 
C)  $- 30.1527 - 51.8731 \mathrm { i }$ 
D)  $5.6015 - 2.1502 \mathrm { i }$ 
A)  $- 51.8731 - 30.1527 \mathrm { i }$ 
B)  $- 2.1502 + 5.6015 \mathrm { i }$ 
C)  $- 30.1527 - 51.8731 \mathrm { i }$ 
D)  $5.6015 - 2.1502 \mathrm { i }$

Question 11

Find an equivalent equation in rectangular coordinates.
-$r = 10 \sin \theta$

Accepted Answer

A)  $\sqrt { x ^ { 2 } + y ^ { 2 } } = 10 x$ 
B)  $x ^ { 2 } + y ^ { 2 } = 10 y$ 
C)  $\sqrt { x ^ { 2 } + y ^ { 2 } } = 10 y$ 
D)  $x ^ { 2 } + y ^ { 2 } = 10 x$ 
A)  $\sqrt { x ^ { 2 } + y ^ { 2 } } = 10 x$ 
B)  $x ^ { 2 } + y ^ { 2 } = 10 y$ 
C)  $\sqrt { x ^ { 2 } + y ^ { 2 } } = 10 y$ 
D)  $x ^ { 2 } + y ^ { 2 } = 10 x$

Question 12

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 20 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) } { 5 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) }$$

Accepted Answer

A)  $- 4 \mathrm { i }$ 
B)  $4 \mathrm { i }$ 
C)  $4 \sqrt { 2 } - 4 \mathrm { i } \sqrt { 2 }$ 
D)  $- 4 \mathrm { i } \sqrt { 2 }$ 
A)  $- 4 \mathrm { i }$ 
B)  $4 \mathrm { i }$ 
C)  $4 \sqrt { 2 } - 4 \mathrm { i } \sqrt { 2 }$ 
D)  $- 4 \mathrm { i } \sqrt { 2 }$

Question 13

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

Accepted Answer

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

Question 14

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
a = 18.6 \mathrm {~cm} \
b = 17.2 \mathrm {~cm} \
c = 15.0 \mathrm {~cm}
\end{array}$$

Accepted Answer

A)  $124 \mathrm {~cm} ^ { 2 }$ 
B)  $121 \mathrm {~cm} ^ { 2 }$ 
C)  $130 \mathrm {~cm} ^ { 2 }$ 
D)  $127 \mathrm {~cm} ^ { 2 }$ 
A)  $124 \mathrm {~cm} ^ { 2 }$ 
B)  $121 \mathrm {~cm} ^ { 2 }$ 
C)  $130 \mathrm {~cm} ^ { 2 }$ 
D)  $127 \mathrm {~cm} ^ { 2 }$

Question 15

Determine whether the pair of vectors is orthogonal.
-$$\langle - 6 , \sqrt { 3 } \rangle , \langle - 2 \sqrt { 3 } , - 12 \rangle$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 16

Find an equivalent equation in rectangular coordinates.
-$\mathrm { r } \sin \theta = 10$

Accepted Answer

A)  $x = 10 y$ 
B)  $y = 10 x$ 
C)  $x = 10$ 
D)  $y = 10$ 
A)  $x = 10 y$ 
B)  $y = 10 x$ 
C)  $x = 10$ 
D)  $y = 10$

Question 17

Find the indicated vector.
-Let $\mathbf { u } = \langle 3,4 \rangle , \mathbf { v } = \langle - 1 , - 5 \rangle$. Find $\mathbf { u } + \mathbf { v }$.

Accepted Answer

A)  $\langle - 2,3 \rangle$ 
B)  $\langle 4,9 \rangle$ 
C)  $\langle 7 , - 6 \rangle$ 
D)  $\langle 2 , - 1 \rangle$ 
A)  $\langle - 2,3 \rangle$ 
B)  $\langle 4,9 \rangle$ 
C)  $\langle 7 , - 6 \rangle$ 
D)  $\langle 2 , - 1 \rangle$

Question 18

Draw a sketch to represent the vector. Refer to the vectors pictured here.  
-$$\frac { 1 } { 2 } \mathbf { a }$$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 19

Determine whether the pair of vectors is orthogonal.
-8, -2 , -3, 5

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 20

Find the indicated angle or side. Give an exact answer.
-Find the exact length of side a.

Accepted Answer

A)  1 
B)  $\sqrt { 13 }$ 
C)  $\sqrt { 61 }$ 
D)  $\sqrt { 73 }$ 
A)  1 
B)  $\sqrt { 13 }$ 
C)  $\sqrt { 61 }$ 
D)  $\sqrt { 73 }$

Find the given power. Write answer in rectangular form. - $( 1 + i ) ^ { 20 }$

Find the given power. Write answer in rectangular form. - $( 1 - i ) ^ { 10 }$

Find an equivalent equation in rectangular coordinates. - $r = \frac { 5 } { 1 + \cos \theta }$

Find the indicated vector. -Let $\mathbf { u } = \langle 5,3 \rangle$ . Find $- 2 \mathbf { u }$ .

Find the given power. Write answer in rectangular form. - $( - \mathrm { i } ) ^ { 11 }$

Find the missing parts of the triangle. - B=15. b=16.58 a=30.83 If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. - $\frac { 60 \left( \cos 150 ^ { \circ } + \mathrm { i } \sin 150 ^ { \circ } \right) } { 10 \left( \cos 39 ^ { \circ } + \mathrm { i } \sin 39 ^ { \circ } \right) }$

Find an equivalent equation in rectangular coordinates. - $r = 10 \sin \theta$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 20 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) } { 5 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) }$

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

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - a=18.6 b=17.2 c=15.0

Determine whether the pair of vectors is orthogonal. - $\langle - 6 , \sqrt { 3 } \rangle , \langle - 2 \sqrt { 3 } , - 12 \rangle$

Find an equivalent equation in rectangular coordinates. - $\mathrm { r } \sin \theta = 10$

Find the indicated vector. -Let $\mathbf { u } = \langle 3,4 \rangle , \mathbf { v } = \langle - 1 , - 5 \rangle$ . Find $\mathbf { u } + \mathbf { v }$ .

Draw a sketch to represent the vector. Refer to the vectors pictured here. $Draw a sketch to represent the vector. Refer to the vectors pictured here. - \frac { 1 } { 2 } \mathbf { a }$ - $\frac { 1 } { 2 } \mathbf { a }$

Determine whether the pair of vectors is orthogonal. -8, -2 , -3, 5

Find the indicated angle or side. Give an exact answer. -Find the exact length of side a.

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

Find the given power. Write answer in rectangular form. - (1+i)20( 1 + i ) ^ { 20 }(1+i)20

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. - x=5tan⁡t,y=4sec⁡t, for t in [0,2π]x=5 \tan t, y=4 \sec t \text {, for } t \text { in }[0,2 \pi]x=5tant,y=4sect, for t in [0,2π]

Find the given power. Write answer in rectangular form. - (1−i)10( 1 - i ) ^ { 10 }(1−i)10

Find an equivalent equation in rectangular coordinates. - r=51+cos⁡θr = \frac { 5 } { 1 + \cos \theta }r=1+cosθ5​

Find the indicated vector. -Let u=⟨5,3⟩\mathbf { u } = \langle 5,3 \rangleu=⟨5,3⟩ . Find −2u- 2 \mathbf { u }−2u .

Find the given power. Write answer in rectangular form. - (−i)11( - \mathrm { i } ) ^ { 11 }(−i)11