Question 1

Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = 3 t , y = t + 7$$

Accepted Answer

A)  $y = \frac { x } { 3 } - 7$ 
B)  $y = 3 x + 7$ 
C)  $y = 3 x - 7$ 
D)  $y = \frac { x } { 3 } + 7$ 
A)  $y = \frac { x } { 3 } - 7$ 
B)  $y = 3 x + 7$ 
C)  $y = 3 x - 7$ 
D)  $y = \frac { x } { 3 } + 7$

Question 2

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

Accepted Answer

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

Question 3

Find the product. Write the product in rectangular form, using exact values.
-$\left[ 7 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) \right] \left[ 2 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right]$

Accepted Answer

A)  $14 \sqrt { 3 } - 14 \mathrm { i }$ 
B)  $- 7 - 7 \sqrt { 3 } i$ 
C)  $5 \sqrt { 6 } - \sqrt { 2 } \mathrm { i }$ 
D)  $7 - 28 \sqrt { 3 } i$ 
A)  $14 \sqrt { 3 } - 14 \mathrm { i }$ 
B)  $- 7 - 7 \sqrt { 3 } i$ 
C)  $5 \sqrt { 6 } - \sqrt { 2 } \mathrm { i }$ 
D)  $7 - 28 \sqrt { 3 } i$

Question 4

Determine the number of triangles ABC possible with the given parts.
-$$a = 34 , b = 69 , A = 75 ^ { \circ }$$

Accepted Answer

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

Question 5

Find the indicated vector.
-Let $\mathbf { a } = 3 \mathrm { i } , \mathbf { b } = \mathbf { i } + \mathrm { j }$. Find $3 \mathbf { a } - \mathbf { b }$.

Accepted Answer

A)  $\mathbf { i } - 8 \mathbf { j }$ 
B)  $8 \mathbf { i } - 3 \mathbf { j }$ 
C)  $11 \mathrm { i } + \mathbf { j }$ 
D)  $8 \mathbf { i } - \mathbf { j }$ 
A)  $\mathbf { i } - 8 \mathbf { j }$ 
B)  $8 \mathbf { i } - 3 \mathbf { j }$ 
C)  $11 \mathrm { i } + \mathbf { j }$ 
D)  $8 \mathbf { i } - \mathbf { j }$

Question 6

Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 5 } - 243 = 0$$

Accepted Answer

A)  $\{ 3 , - 3 \}$ 
B)  $\left\{ 3 \operatorname { cis } 0,3 \operatorname { cis } \frac { 2 \pi } { 5 } , 3 \operatorname { cis } \frac { 4 \pi } { 5 } , 3 \operatorname { cis } \frac { 6 \pi } { 5 } , 3 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}$ 
C)  $\left\{ 243 \operatorname { cis } 0,243 \operatorname { cis } \frac { 2 \pi } { 5 } , 243 \operatorname { cis } \frac { 4 \pi } { 5 } , 243 \operatorname { cis } \frac { 6 \pi } { 5 } , 243 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}$ 
D)  $\left\{ 3 \operatorname { cis } \frac { \pi } { 5 } , 3 \operatorname { cis } \frac { 3 \pi } { 5 } , 3 \right.$ cis $\pi , 3$ cis $\frac { 7 \pi } { 5 } , 3$ cis $\left. \frac { 9 \pi } { 5 } \right\}$ 
A)  $\{ 3 , - 3 \}$ 
B)  $\left\{ 3 \operatorname { cis } 0,3 \operatorname { cis } \frac { 2 \pi } { 5 } , 3 \operatorname { cis } \frac { 4 \pi } { 5 } , 3 \operatorname { cis } \frac { 6 \pi } { 5 } , 3 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}$ 
C)  $\left\{ 243 \operatorname { cis } 0,243 \operatorname { cis } \frac { 2 \pi } { 5 } , 243 \operatorname { cis } \frac { 4 \pi } { 5 } , 243 \operatorname { cis } \frac { 6 \pi } { 5 } , 243 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}$ 
D)  $\left\{ 3 \operatorname { cis } \frac { \pi } { 5 } , 3 \operatorname { cis } \frac { 3 \pi } { 5 } , 3 \right.$ cis $\pi , 3$ cis $\frac { 7 \pi } { 5 } , 3$ cis $\left. \frac { 9 \pi } { 5 } \right\}$

Question 7

The graph of r = aθ in polar coordinates is an example of the spiral of Archimedes. With your calculator set to radian
mode, use the given value of a and interval of θ to graph the spiral in the window specified.
-$\mathrm{a}=-0.5,-\pi \leq \theta \leq 4 \pi,[-6,6] \text { by }[-6,6]$

Accepted Answer

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

Question 8

Solve the problem.
-A projectile is fired with an initial velocity of 450 feet per second at an angle of $$70 ^ { \circ }$$ with the horizontal. To the nearest 10 feet, find the horizontal distance covered by the projectile.

Accepted Answer

A)  4310 ft 
B)  3930 ft 
C)  4070 ft 
D)  4180 ft 
A)  4310 ft 
B)  3930 ft 
C)  4070 ft 
D)  4180 ft

Question 9

Find all cube roots of the complex number. Leave answers in trigonometric form.
-$$- 64 i$$

Accepted Answer

A)  $4 \operatorname { cis } 90 ^ { \circ } , 4$ cis $^ { \circ } 210,4$ cis $330 ^ { \circ }$ 
B)  4 cis $90 ^ { \circ } , 4 \operatorname { cis } ^ { \circ } 180,4$ cis $270 ^ { \circ }$ 
C)  $4 \operatorname { cis } 30 ^ { \circ } , 4$ cis $^ { \circ } 60,4 \operatorname { cis } 90 ^ { \circ }$ 
D)  4 cis ${ } ^ { \circ } 210 , , 4 \operatorname { cis } 270 ^ { \circ } , 4 \operatorname { cis } 330 ^ { \circ }$ 
A)  $4 \operatorname { cis } 90 ^ { \circ } , 4$ cis $^ { \circ } 210,4$ cis $330 ^ { \circ }$ 
B)  4 cis $90 ^ { \circ } , 4 \operatorname { cis } ^ { \circ } 180,4$ cis $270 ^ { \circ }$ 
C)  $4 \operatorname { cis } 30 ^ { \circ } , 4$ cis $^ { \circ } 60,4 \operatorname { cis } 90 ^ { \circ }$ 
D)  4 cis ${ } ^ { \circ } 210 , , 4 \operatorname { cis } 270 ^ { \circ } , 4 \operatorname { cis } 330 ^ { \circ }$

Question 10

Solve the problem.
-A projectile is fired with an initial velocity of 600 feet per second at an angle of 45° with the horizontal. To the nearest foot, find the maximum altitude of the projectile.

Accepted Answer

A)  2804 ft 
B)  2812 ft 
C)  2828 ft 
D)  2795 ft 
A)  2804 ft 
B)  2812 ft 
C)  2828 ft 
D)  2795 ft

Question 11

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth.
-

Accepted Answer

A)  $\langle - 14.98 , - 43.49 \rangle$ 
B)  $\langle - 15.84 , - 46 \rangle$ 
C)  $\langle - 0.33 , - 0.95 \rangle$ 
D)  $\langle - 43.49 , - 14.98 \rangle$ 
A)  $\langle - 14.98 , - 43.49 \rangle$ 
B)  $\langle - 15.84 , - 46 \rangle$ 
C)  $\langle - 0.33 , - 0.95 \rangle$ 
D)  $\langle - 43.49 , - 14.98 \rangle$

Question 12

Solve the problem.
-Given that the polar equation $\mathrm { r } = \frac { \mathrm { a } \left( 1 - \mathrm { e } ^ { 2 } \right) } { 1 + \mathrm { e } \cos \theta }$ models the orbits of the planets about the sun, estimate the closest possible approach of a planet for which $\mathrm { a } = 18$ and $\mathrm { e } = 0.6$ to a planet for which $a = 45$ and $\mathrm { e } = 0.030$.

Accepted Answer

A)  18 astronomical units 
B)  0 astronomical units 
C)  75 astronomical units 
D)  36 astronomical units 
A)  18 astronomical units 
B)  0 astronomical units 
C)  75 astronomical units 
D)  36 astronomical units

Question 13

Find the missing parts of the triangle.
- 
If necessary, round angles to the nearest degree and give exact values of side lengths.

Accepted Answer

A)  $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 4 \sqrt { 3 }$ 
B)  no such triangle 
C)  $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 4 \sqrt { 3 } + 4$ 
D)  $\mathrm { A } = 75 ^ { \circ } , \mathrm { C } = 45 ^ { \circ } , \mathrm { c } = 4 \sqrt { 3 } + 4$ 
A)  $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 4 \sqrt { 3 }$ 
B)  no such triangle 
C)  $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 4 \sqrt { 3 } + 4$ 
D)  $\mathrm { A } = 75 ^ { \circ } , \mathrm { C } = 45 ^ { \circ } , \mathrm { c } = 4 \sqrt { 3 } + 4$

Question 14

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

Accepted Answer

A)   
B)   
A)   
B)

Question 15

For the given rectangular equation, give its equivalent polar equation.
-$$8 x - 5 y = - 14$$

Accepted Answer

A)  $r = \frac { - 14 } { 8 \cos \theta - 5 \sin \theta }$ 
B)  $r = \frac { - 14 } { 8 \cos \theta + 5 \sin \theta }$ 
C)  $\mathrm { r } = \frac { - 14 } { 8 \sin \theta - 5 \cos \theta }$ 
D)  $r = \frac { - 14 } { 5 \cos \theta - 8 \sin \theta }$ 
A)  $r = \frac { - 14 } { 8 \cos \theta - 5 \sin \theta }$ 
B)  $r = \frac { - 14 } { 8 \cos \theta + 5 \sin \theta }$ 
C)  $\mathrm { r } = \frac { - 14 } { 8 \sin \theta - 5 \cos \theta }$ 
D)  $r = \frac { - 14 } { 5 \cos \theta - 8 \sin \theta }$

Question 16

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular
equation for the curve.
-

Accepted Answer

A) 
 
$y = \frac { 1 } { 3 } x + 1$, for $x$ in $[ - 6,9 ]$ 
B) 
 
$y = - 3 x + 1$, for $x$ in $[ - 9,6 ]$ 
C) 
 
$y = x ^ { 2 } + 1$, for $x$ in $[ - 2,2 ]$ 
D) 
 
$$y = \frac { 1 } { 3 } x - 1 , \text { for } x \text { in } [ - 6,9 ]$$ 
A) 
 
$y = \frac { 1 } { 3 } x + 1$, for $x$ in $[ - 6,9 ]$ 
B) 
 
$y = - 3 x + 1$, for $x$ in $[ - 9,6 ]$ 
C) 
 
$y = x ^ { 2 } + 1$, for $x$ in $[ - 2,2 ]$ 
D) 
 
$$y = \frac { 1 } { 3 } x - 1 , \text { for } x \text { in } [ - 6,9 ]$$

Question 17

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { C } = 90 ^ { \circ } \
\mathrm { c } = 24 \mathrm {~m} \
\mathrm { a } = 48 \mathrm {~m}
\end{array}$$
If necessary, round angles to the nearest degree and give exact values of side lengths.

Accepted Answer

A)  $\mathrm { A } = 30 ^ { \circ } , \mathrm { B } = 60 ^ { \circ } , \mathrm { b } = 24 \sqrt { 3 } \mathrm {~m}$ 
B)  $\mathrm { A } = 60 ^ { \circ } , \mathrm { B } = 30 ^ { \circ } , \mathrm { b } = 24 \sqrt { 3 } \mathrm {~m}$ 
C)  no such triangle 
D)  $A = 30 ^ { \circ } , B = 60 ^ { \circ } , b = 24 \sqrt { 2 } \mathrm {~m}$ 
A)  $\mathrm { A } = 30 ^ { \circ } , \mathrm { B } = 60 ^ { \circ } , \mathrm { b } = 24 \sqrt { 3 } \mathrm {~m}$ 
B)  $\mathrm { A } = 60 ^ { \circ } , \mathrm { B } = 30 ^ { \circ } , \mathrm { b } = 24 \sqrt { 3 } \mathrm {~m}$ 
C)  no such triangle 
D)  $A = 30 ^ { \circ } , B = 60 ^ { \circ } , b = 24 \sqrt { 2 } \mathrm {~m}$

Question 18

Find sum of the pair of complex numbers.
-$5 + 2 i , 4 i$

Accepted Answer

A)  $5 + 8 \mathrm { i }$ 
B)  $5 - 2 i$ 
C)  $5 - 8 \mathrm { i }$ 
D)  $5 + 6 i$ 
A)  $5 + 8 \mathrm { i }$ 
B)  $5 - 2 i$ 
C)  $5 - 8 \mathrm { i }$ 
D)  $5 + 6 i$

Question 19

Find the indicated vector.
-Let $\mathbf { a } = \langle 8,4 \rangle , \mathbf { b } = \langle - 3 , - 2 \rangle$. Find $\mathbf { a } + \mathbf { b }$.

Accepted Answer

A)  $\langle 12 , - 5 \rangle$ 
B)  $\langle 11,6 \rangle$ 
C)  $\langle 6,1 \rangle$ 
D)  $\langle 5,2 \rangle$ 
A)  $\langle 12 , - 5 \rangle$ 
B)  $\langle 11,6 \rangle$ 
C)  $\langle 6,1 \rangle$ 
D)  $\langle 5,2 \rangle$

Question 20

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 2 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) } { 4 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right) }$$

Accepted Answer

A)  $\frac { 1 } { 4 } - \frac { 1 } { 4 } \mathrm { i } \sqrt { 3 }$ 
B)  $\frac { 1 } { 4 } + \frac { 1 } { 4 } \mathrm { i } \sqrt { 3 }$ 
C)  $\frac { 1 } { 2 } \sqrt { 3 } - \frac { 1 } { 4 } \mathrm { i }$ 
D)  $\frac { 1 } { 2 } \sqrt { 3 } + \frac { 1 } { 4 } \mathrm { i }$ 
A)  $\frac { 1 } { 4 } - \frac { 1 } { 4 } \mathrm { i } \sqrt { 3 }$ 
B)  $\frac { 1 } { 4 } + \frac { 1 } { 4 } \mathrm { i } \sqrt { 3 }$ 
C)  $\frac { 1 } { 2 } \sqrt { 3 } - \frac { 1 } { 4 } \mathrm { i }$ 
D)  $\frac { 1 } { 2 } \sqrt { 3 } + \frac { 1 } { 4 } \mathrm { i }$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = 3 t , y = t + 7$

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

Find the product. Write the product in rectangular form, using exact values. - $\left[ 7 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) \right] \left[ 2 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right]$

Determine the number of triangles ABC possible with the given parts. - $a = 34 , b = 69 , A = 75 ^ { \circ }$

Find the indicated vector. -Let $\mathbf { a } = 3 \mathrm { i } , \mathbf { b } = \mathbf { i } + \mathrm { j }$ . Find $3 \mathbf { a } - \mathbf { b }$ .

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 5 } - 243 = 0$

The graph of r = aθ in polar coordinates is an example of the spiral of Archimedes. With your calculator set to radian mode, use the given value of a and interval of θ to graph the spiral in the window specified. - $\mathrm{a}=-0.5,-\pi \leq \theta \leq 4 \pi,[-6,6] \text { by }[-6,6]$

Solve the problem. -A projectile is fired with an initial velocity of 450 feet per second at an angle of $70 ^ { \circ }$ with the horizontal. To the nearest 10 feet, find the horizontal distance covered by the projectile.

Find all cube roots of the complex number. Leave answers in trigonometric form. - $- 64 i$

Solve the problem. -A projectile is fired with an initial velocity of 600 feet per second at an angle of 45° with the horizontal. To the nearest foot, find the maximum altitude of the projectile.

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Find the missing parts of the triangle. - If necessary, round angles to the nearest degree and give exact values of side lengths.

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

For the given rectangular equation, give its equivalent polar equation. - $8 x - 5 y = - 14$

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. -

Find the missing parts of the triangle. - =9 =24 =48 If necessary, round angles to the nearest degree and give exact values of side lengths.

Find sum of the pair of complex numbers. - $5 + 2 i , 4 i$

Find the indicated vector. -Let $\mathbf { a } = \langle 8,4 \rangle , \mathbf { b } = \langle - 3 , - 2 \rangle$ . Find $\mathbf { a } + \mathbf { b }$ .

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 2 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) } { 4 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right) }$

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

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Exam 8: Applications of Trigonometry

Find a rectangular equation for the plane curve defined by the parametric equations. - x=3t,y=t+7x = 3 t , y = t + 7x=3t,y=t+7

Find an equivalent equation in rectangular coordinates. - r=10sin⁡θr = 10 \sin \thetar=10sinθ

Determine the number of triangles ABC possible with the given parts. - a=34,b=69,A=75∘a = 34 , b = 69 , A = 75 ^ { \circ }a=34,b=69,A=75∘

Find the indicated vector. -Let a=3i,b=i+j\mathbf { a } = 3 \mathrm { i } , \mathbf { b } = \mathbf { i } + \mathrm { j }a=3i,b=i+j . Find 3a−b3 \mathbf { a } - \mathbf { b }3a−b .

Find all solutions of the equation. Leave answers in trigonometric form. - x5−243=0x ^ { 5 } - 243 = 0x5−243=0

Solve the problem. -A projectile is fired with an initial velocity of 450 feet per second at an angle of 70∘70 ^ { \circ }70∘ with the horizontal. To the nearest 10 feet, find the horizontal distance covered by the projectile.

Find all cube roots of the complex number. Leave answers in trigonometric form. - −64i- 64 i−64i