Question 1

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
\mathrm { a } = 14.5 \mathrm {~cm} \
\mathrm {~b} = 14.3 \mathrm {~cm} \
\mathrm { c } = 13.1 \mathrm {~cm}
\end{array}$$

Accepted Answer

A)  $87 \mathrm {~cm} ^ { 2 }$ 
B)  $84 \mathrm {~cm} ^ { 2 }$ 
C)  $93 \mathrm {~cm} ^ { 2 }$ 
D)  $90 \mathrm {~cm} ^ { 2 }$ 
A)  $87 \mathrm {~cm} ^ { 2 }$ 
B)  $84 \mathrm {~cm} ^ { 2 }$ 
C)  $93 \mathrm {~cm} ^ { 2 }$ 
D)  $90 \mathrm {~cm} ^ { 2 }$

Question 2

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°].
-$\langle - 8,0 \rangle$

Accepted Answer

A)  $8 ; 180 ^ { \circ }$ 
B)  $8 ; 270 ^ { \circ }$ 
C)  $64 ; 180 ^ { \circ }$ 
D)  $8 ; 90 ^ { \circ }$ 
A)  $8 ; 180 ^ { \circ }$ 
B)  $8 ; 270 ^ { \circ }$ 
C)  $64 ; 180 ^ { \circ }$ 
D)  $8 ; 90 ^ { \circ }$

Question 3

Solve the problem.
-Two forces, of $67.7$ and $15.8 \mathrm { lb }$, forming an angle of $26.7 ^ { \circ }$, act at a point in the plane. Find the magnitude of the resultant force.

Accepted Answer

A)  $54.1 \mathrm { lb }$ 
B)  $82.1 \mathrm { lb }$ 
C)  $500 \mathrm { lb }$ 
D)  $83.5 \mathrm { lb }$ 
A)  $54.1 \mathrm { lb }$ 
B)  $82.1 \mathrm { lb }$ 
C)  $500 \mathrm { lb }$ 
D)  $83.5 \mathrm { lb }$

Question 4

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°].
-$$\langle - 4 , - 3 \rangle$$

Accepted Answer

A)  $7 ; 216.9 ^ { \circ }$ 
B)  $5 ; 36.9 ^ { \circ }$ 
C)  $5 ; 233.1 ^ { \circ }$ 
D)  $5 ; 216.9 ^ { \circ }$ 
A)  $7 ; 216.9 ^ { \circ }$ 
B)  $5 ; 36.9 ^ { \circ }$ 
C)  $5 ; 233.1 ^ { \circ }$ 
D)  $5 ; 216.9 ^ { \circ }$

Question 5

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

Accepted Answer

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

Question 6

Find a rectangular equation for the plane curve defined by the parametric equations.
-$$\mathrm { x } = \mathrm { t } - 3 , \mathrm { y } = \mathrm { t } ^ { 2 } + 5$$

Accepted Answer

A)  $y = x ^ { 2 } + 6 x + 14$ 
B)  $y = x ^ { 2 } - 14$ 
C)  $y = x ^ { 2 } + 14$ 
D)  $y = x ^ { 2 } - 6 x - 14$ 
A)  $y = x ^ { 2 } + 6 x + 14$ 
B)  $y = x ^ { 2 } - 14$ 
C)  $y = x ^ { 2 } + 14$ 
D)  $y = x ^ { 2 } - 6 x - 14$

Question 7

Graph the cycloid for t in the indicated interval.
-$$x = 3 ( t - \sin t ) , y = 3 ( 1 - \cos t ) , 0 \leq t \leq 6 \pi$$

Accepted Answer

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

Question 8

Write the complex number in rectangular form.
-$9 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right)$

Accepted Answer

A)  $- 9$ 
B)  $- 9 \mathrm { i }$ 
C)  9 
D)  $9 \mathrm { i }$ 
A)  $- 9$ 
B)  $- 9 \mathrm { i }$ 
C)  9 
D)  $9 \mathrm { i }$

Question 9

Solve the problem.
-If $\mathbf { u } = \langle - 5,3 \rangle , \mathbf { v } = \langle 6 , - 6 \rangle$, and $\mathbf { w } = \langle - 3,12 \rangle$, evaluate $( \mathbf { u } + \mathbf { v } ) \cdot \mathbf { w }$.

Accepted Answer

A)  $- 43$ 
B)  $- 39$ 
C)  $- 34$ 
D)  $- 32$ 
A)  $- 43$ 
B)  $- 39$ 
C)  $- 34$ 
D)  $- 32$

Question 10

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

Accepted Answer

A)   
B)   
A)   
B)

Question 11

Find an equivalent equation in rectangular coordinates.
-$\mathrm { r } ( \cos \theta - \sin \theta ) = 5$

Accepted Answer

A)  $x - y = 5$ 
B)  $\sqrt { x ^ { 2 } + y ^ { 2 } } ( x - y ) = 5$ 
C)  $x + y = 5$ 
D)  $x - y = 25$ 
A)  $x - y = 5$ 
B)  $\sqrt { x ^ { 2 } + y ^ { 2 } } ( x - y ) = 5$ 
C)  $x + y = 5$ 
D)  $x - y = 25$

Question 12

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { A } = 21 ^ { \circ } \
\mathrm { a } = 35 \mathrm {~km} \
\mathrm {~b} = 50 \mathrm {~km}
\end{array}$$
If necessary, round angles to the nearest whole number and side lengths to the nearest $\mathrm { km }$.

Accepted Answer

A)  $\mathrm { B } _ { 1 } = 128 ^ { \circ } , \mathrm { C } _ { 1 } = 31 ^ { \circ } , \mathrm { c } _ { 1 } = 77 \mathrm {~km}$ 
B)  $\mathrm { B } = 31 ^ { \circ } , \mathrm { C } = 128 ^ { \circ } , \mathrm { c } = 77 \mathrm {~km}$
$$\mathrm { B } _ { 2 } = 10 ^ { \circ } , \mathrm { C } _ { 2 } = 149 ^ { \circ } , \mathrm { c } _ { 2 } = 17 \mathrm {~km}$$ 
C)  no such triangle 
D)  $\mathrm { B } _ { 1 } = 31 ^ { \circ } , \mathrm { C } _ { 1 } = 128 ^ { \circ } , \mathrm { c } _ { 1 } = 77 \mathrm {~km}$
$$\mathrm { B } _ { 2 } = 149 ^ { \circ } , \mathrm { C } _ { 2 } = 10 ^ { \circ } , \mathrm { c } _ { 2 } = 17 \mathrm {~km}$$ 
A)  $\mathrm { B } _ { 1 } = 128 ^ { \circ } , \mathrm { C } _ { 1 } = 31 ^ { \circ } , \mathrm { c } _ { 1 } = 77 \mathrm {~km}$ 
B)  $\mathrm { B } = 31 ^ { \circ } , \mathrm { C } = 128 ^ { \circ } , \mathrm { c } = 77 \mathrm {~km}$
$$\mathrm { B } _ { 2 } = 10 ^ { \circ } , \mathrm { C } _ { 2 } = 149 ^ { \circ } , \mathrm { c } _ { 2 } = 17 \mathrm {~km}$$ 
C)  no such triangle 
D)  $\mathrm { B } _ { 1 } = 31 ^ { \circ } , \mathrm { C } _ { 1 } = 128 ^ { \circ } , \mathrm { c } _ { 1 } = 77 \mathrm {~km}$
$$\mathrm { B } _ { 2 } = 149 ^ { \circ } , \mathrm { C } _ { 2 } = 10 ^ { \circ } , \mathrm { c } _ { 2 } = 17 \mathrm {~km}$$

Question 13

Find the dot product for the pair of vectors.
-$$\langle - 12,8 \rangle , \langle 0,7 \rangle$$

Accepted Answer

A)  $- 84$ 
B)  68 
C)  56 
D)  44 
A)  $- 84$ 
B)  68 
C)  56 
D)  44

Question 14

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°].
-$\langle - 12,5 \rangle$

Accepted Answer

A)  $13 ; 112.6 ^ { \circ }$ 
B)  $13 ; 22.6 ^ { \circ }$ 
C)  $13 ; 157.4 ^ { \circ }$ 
D)  $15 ; 157.4 ^ { \circ }$ 
A)  $13 ; 112.6 ^ { \circ }$ 
B)  $13 ; 22.6 ^ { \circ }$ 
C)  $13 ; 157.4 ^ { \circ }$ 
D)  $15 ; 157.4 ^ { \circ }$

Question 15

Find the component form of the indicated vector.
-Let $\mathbf { u } = \langle - 6 , - 1 \rangle$. Find $8 \mathbf { u }$.

Accepted Answer

A)  $\langle - 48 , - 8 \rangle$ 
B)  $\langle 48,8 \rangle$ 
C)  $\langle - 48,8 \rangle$ 
D)  $\langle 48 , - 8 \rangle$ 
A)  $\langle - 48 , - 8 \rangle$ 
B)  $\langle 48,8 \rangle$ 
C)  $\langle - 48,8 \rangle$ 
D)  $\langle 48 , - 8 \rangle$

Question 16

Graph the cycloid for t in the indicated interval.
-$$x = 5 ( t - \sin t ) , y = 5 ( 1 - \cos t ) , 0 \leq t \leq 4 \pi$$

Accepted Answer

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

Question 17

For the given rectangular equation, give its equivalent polar equation.
-$$2 x + 3 y = 6$$

Accepted Answer

A)  $r = \frac { 2 \cos \theta + 3 \sin \theta } { 6 }$ 
B)  $r = \frac { 2 \sin \theta + 3 \cos \theta } { 6 }$ 
C)  $r = \frac { 6 } { 2 \sin \theta + 3 \cos \theta }$ 
D)  $r = \frac { 6 } { 2 \cos \theta + 3 \sin \theta }$ 
A)  $r = \frac { 2 \cos \theta + 3 \sin \theta } { 6 }$ 
B)  $r = \frac { 2 \sin \theta + 3 \cos \theta } { 6 }$ 
C)  $r = \frac { 6 } { 2 \sin \theta + 3 \cos \theta }$ 
D)  $r = \frac { 6 } { 2 \cos \theta + 3 \sin \theta }$

Question 18

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

Accepted Answer

A)  9 
B)  $\sqrt { 47 }$ 
C)  $\sqrt { 109 }$ 
D)  7 
A)  9 
B)  $\sqrt { 47 }$ 
C)  $\sqrt { 109 }$ 
D)  7

Question 19

Find all specified roots.
-Seventh roots of $1 .$

Accepted Answer

A)  $- 1 , \operatorname { cis } \frac { \pi } { 7 } , \operatorname { cis } \frac { 2 \pi } { 7 } , \operatorname { cis } \frac { 3 \pi } { 7 } , \operatorname { cis } \frac { 4 \pi } { 7 } , \operatorname { cis } \frac { 5 \pi } { 7 } , \operatorname { cis } \frac { 6 \pi } { 7 }$ 
B)  $1 , \operatorname { cis } \frac { 2 \pi } { 7 } , \operatorname { cis } \frac { 4 \pi } { 7 } , \operatorname { cis } \frac { 6 \pi } { 7 } , \operatorname { cis } \frac { 8 \pi } { 7 } , \operatorname { cis } \frac { 10 \pi } { 7 } , \operatorname { cis } \frac { 12 \pi } { 7 } , - 1$ 
C)  $1 , \operatorname { cis } \frac { 2 \pi } { 7 } , \operatorname { cis } \frac { 4 \pi } { 7 } , \operatorname { cis } \frac { 6 \pi } { 7 } , \operatorname { cis } \frac { 8 \pi } { 7 } , \operatorname { cis } \frac { 10 \pi } { 7 } , \operatorname { cis } \frac { 12 \pi } { 7 }$ 
D)  $1 , \operatorname { cis } \frac { \pi } { 7 } , \operatorname { cis } \frac { 2 \pi } { 7 } , \operatorname { cis } \frac { 3 \pi } { 7 } , \operatorname { cis } \frac { 4 \pi } { 7 } , \operatorname { cis } \frac { 5 \pi } { 7 } , \operatorname { cis } \frac { 6 \pi } { 7 }$ 
A)  $- 1 , \operatorname { cis } \frac { \pi } { 7 } , \operatorname { cis } \frac { 2 \pi } { 7 } , \operatorname { cis } \frac { 3 \pi } { 7 } , \operatorname { cis } \frac { 4 \pi } { 7 } , \operatorname { cis } \frac { 5 \pi } { 7 } , \operatorname { cis } \frac { 6 \pi } { 7 }$ 
B)  $1 , \operatorname { cis } \frac { 2 \pi } { 7 } , \operatorname { cis } \frac { 4 \pi } { 7 } , \operatorname { cis } \frac { 6 \pi } { 7 } , \operatorname { cis } \frac { 8 \pi } { 7 } , \operatorname { cis } \frac { 10 \pi } { 7 } , \operatorname { cis } \frac { 12 \pi } { 7 } , - 1$ 
C)  $1 , \operatorname { cis } \frac { 2 \pi } { 7 } , \operatorname { cis } \frac { 4 \pi } { 7 } , \operatorname { cis } \frac { 6 \pi } { 7 } , \operatorname { cis } \frac { 8 \pi } { 7 } , \operatorname { cis } \frac { 10 \pi } { 7 } , \operatorname { cis } \frac { 12 \pi } { 7 }$ 
D)  $1 , \operatorname { cis } \frac { \pi } { 7 } , \operatorname { cis } \frac { 2 \pi } { 7 } , \operatorname { cis } \frac { 3 \pi } { 7 } , \operatorname { cis } \frac { 4 \pi } { 7 } , \operatorname { cis } \frac { 5 \pi } { 7 } , \operatorname { cis } \frac { 6 \pi } { 7 }$

Question 20

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-[8( $\left. \left. \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) \right] \left[ 3 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right]$

Accepted Answer

A)  $- 5.5000 + 9.5263 \mathrm { i }$ 
B)  $- 0.5000 + 0.8660 \mathrm { i }$ 
C)  $- 12.000 + 20.7846 \mathrm { i }$ 
D)  $- 1.0000 + 1.7321 \mathrm { i }$ 
A)  $- 5.5000 + 9.5263 \mathrm { i }$ 
B)  $- 0.5000 + 0.8660 \mathrm { i }$ 
C)  $- 12.000 + 20.7846 \mathrm { i }$ 
D)  $- 1.0000 + 1.7321 \mathrm { i }$

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - =14.5 =14.3 =13.1

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. - $\langle - 8,0 \rangle$

Solve the problem. -Two forces, of $67.7$ and $15.8 \mathrm { lb }$ , forming an angle of $26.7 ^ { \circ }$ , act at a point in the plane. Find the magnitude of the resultant force.

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. - $\langle - 4 , - 3 \rangle$

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

Find a rectangular equation for the plane curve defined by the parametric equations. - $\mathrm { x } = \mathrm { t } - 3 , \mathrm { y } = \mathrm { t } ^ { 2 } + 5$

Graph the cycloid for t in the indicated interval. - $x = 3 ( t - \sin t ) , y = 3 ( 1 - \cos t ) , 0 \leq t \leq 6 \pi$ $Graph the cycloid for t in the indicated interval. - x = 3 ( t - \sin t ) , y = 3 ( 1 - \cos t ) , 0 \leq t \leq 6 \pi$

Write the complex number in rectangular form. - $9 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right)$

Solve the problem. -If $\mathbf { u } = \langle - 5,3 \rangle , \mathbf { v } = \langle 6 , - 6 \rangle$ , and $\mathbf { w } = \langle - 3,12 \rangle$ , evaluate $( \mathbf { u } + \mathbf { v } ) \cdot \mathbf { w }$ .

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

Find an equivalent equation in rectangular coordinates. - $\mathrm { r } ( \cos \theta - \sin \theta ) = 5$

Find the missing parts of the triangle. - =2 =35 =50 If necessary, round angles to the nearest whole number and side lengths to the nearest $\mathrm { km }$ .

Find the dot product for the pair of vectors. - $\langle - 12,8 \rangle , \langle 0,7 \rangle$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. - $\langle - 12,5 \rangle$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 6 , - 1 \rangle$ . Find $8 \mathbf { u }$ .

Graph the cycloid for t in the indicated interval. - $x = 5 ( t - \sin t ) , y = 5 ( 1 - \cos t ) , 0 \leq t \leq 4 \pi$ $Graph the cycloid for t in the indicated interval. - x = 5 ( t - \sin t ) , y = 5 ( 1 - \cos t ) , 0 \leq t \leq 4 \pi$

For the given rectangular equation, give its equivalent polar equation. - $2 x + 3 y = 6$

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

Find all specified roots. -Seventh roots of $1 .$

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. -[8( $\left. \left. \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) \right] \left[ 3 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right]$

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Inverse, Exponential, and Logarithmic Functions

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Exam 8: Applications of Trigonometry

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - =14.5 =14.3 =13.1

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. - ⟨−8,0⟩\langle - 8,0 \rangle⟨−8,0⟩

Solve the problem. -Two forces, of 67.767.767.7 and 15.8lb15.8 \mathrm { lb }15.8lb , forming an angle of 26.7∘26.7 ^ { \circ }26.7∘ , act at a point in the plane. Find the magnitude of the resultant force.

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. - ⟨−4,−3⟩\langle - 4 , - 3 \rangle⟨−4,−3⟩

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

Find a rectangular equation for the plane curve defined by the parametric equations. - x=t−3,y=t2+5\mathrm { x } = \mathrm { t } - 3 , \mathrm { y } = \mathrm { t } ^ { 2 } + 5x=t−3,y=t2+5

Graph the cycloid for t in the indicated interval. - x=3(t−sin⁡t),y=3(1−cos⁡t),0≤t≤6πx = 3 ( t - \sin t ) , y = 3 ( 1 - \cos t ) , 0 \leq t \leq 6 \pix=3(t−sint),y=3(1−cost),0≤t≤6π

Write the complex number in rectangular form. - 9(cos⁡180∘+isin⁡180∘)9 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right)9(cos180∘+isin180∘)