Question 1

Use the dot product to find the magnitude of u if $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$

Accepted Answer

A)  $\| \mathbf { u } \| = 18$ 
B)  $\| \mathbf { u } \| =$ $6 \sqrt { 5 }$ 
C)  $\| \mathbf { u } \| = 18$. 
D)   $\| \mathbf { u } \| =$ $3 \sqrt { 5 }$ 
E)  $\| \mathbf { u } \| = 23$ 
A)  $\| \mathbf { u } \| = 18$ 
B)  $\| \mathbf { u } \| =$ $6 \sqrt { 5 }$ 
C)  $\| \mathbf { u } \| = 18$. 
D)   $\| \mathbf { u } \| =$ $3 \sqrt { 5 }$ 
E)  $\| \mathbf { u } \| = 23$

Question 2

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​
A = 78.2, b = 52, c = 52
​

Accepted Answer

A) 771.91 
B) ​140.43 
C) ​80.66 
D) ​769.91 
E) 1340.39 
A) 771.91 
B) ​140.43 
C) ​80.66 
D) ​769.91 
E) 1340.39

Question 3

Multiply the complex numbers below and leave the result in trigonometric form.   $\left[ 8 \left( \cos \frac { 2 \pi } { 7 } + i \sin \frac { 2 \pi } { 7 } \right) \right] \left[ 10 \left( \cos \frac { 5 \pi } { 9 } + i \sin \frac { 5 \pi } { 9 } \right) \right]$

Accepted Answer

A)  $18 \left( \cos \frac { 53 } { 63 } \pi + i \sin \frac { 53 } { 63 } \pi \right)$ 
B)   $80 \left( \cos \frac { 23 } { 63 } \pi + i \sin \frac { 23 } { 63 } \pi \right)$ 
C)   $80 \left( \cos \frac { 53 } { 63 } \pi + i \sin \frac { 53 } { 63 } \pi \right)$ 
D)   $18 \left( \cos \frac { 1 } { 9 } \pi + i \sin \frac { 1 } { 9 } \pi \right)$ 
E)  $80 \left( \cos \frac { 1 } { 9 } \pi + i \sin \frac { 1 } { 9 } \pi \right)$ 
A)  $18 \left( \cos \frac { 53 } { 63 } \pi + i \sin \frac { 53 } { 63 } \pi \right)$ 
B)   $80 \left( \cos \frac { 23 } { 63 } \pi + i \sin \frac { 23 } { 63 } \pi \right)$ 
C)   $80 \left( \cos \frac { 53 } { 63 } \pi + i \sin \frac { 53 } { 63 } \pi \right)$ 
D)   $18 \left( \cos \frac { 1 } { 9 } \pi + i \sin \frac { 1 } { 9 } \pi \right)$ 
E)  $80 \left( \cos \frac { 1 } { 9 } \pi + i \sin \frac { 1 } { 9 } \pi \right)$

Question 4

Find the standard form of the complex number shown below. $5 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$

Accepted Answer

A)  $- \frac { 5 \sqrt { 3 } } { 2 } - \frac { 5 } { 2 }$ 
B)  $\frac { 5 \sqrt { 3 } } { 4 } - \frac { 5 } { 4 }$ 
C)  $\frac { 2 } { 5 } - \frac { 2 \sqrt { 3 } } { 5 }$ 
D)  $\frac { 5 \sqrt { 3 } } { 2 } - \frac { 5 } { 2 }$ 
E)  $\frac { 5 \sqrt { 3 } } { 4 } + \frac { 5 } { 4 }$ 
A)  $- \frac { 5 \sqrt { 3 } } { 2 } - \frac { 5 } { 2 }$ 
B)  $\frac { 5 \sqrt { 3 } } { 4 } - \frac { 5 } { 4 }$ 
C)  $\frac { 2 } { 5 } - \frac { 2 \sqrt { 3 } } { 5 }$ 
D)  $\frac { 5 \sqrt { 3 } } { 2 } - \frac { 5 } { 2 }$ 
E)  $\frac { 5 \sqrt { 3 } } { 4 } + \frac { 5 } { 4 }$

Question 5

Plot the complex number 2.   ​

Accepted Answer

A)    
B)    ​ 
C)    
D)    
E)    
A)    
B)    ​ 
C)    
D)    
E)

Question 6

Find the projection of u onto v. 
 $\begin{array} { l } 
\mathbf { u } = \langle 0,4 \rangle \
\mathbf { v } = \langle 3,20 \rangle
\end{array}$

Accepted Answer

A)  $\frac { 1 } { 409 } \langle 0,3 \rangle$ 
B)  $409 \langle 1600,240 \rangle$ 
C)  $\frac { 80 } { 409 } \langle 240,1600 \rangle$ 
D)  $\frac { 409 } { 80 } \langle 240,1600 \rangle$ 
E)  $\frac { 1 } { 409 } \langle 240,1600 \rangle$ 
A)  $\frac { 1 } { 409 } \langle 0,3 \rangle$ 
B)  $409 \langle 1600,240 \rangle$ 
C)  $\frac { 80 } { 409 } \langle 240,1600 \rangle$ 
D)  $\frac { 409 } { 80 } \langle 240,1600 \rangle$ 
E)  $\frac { 1 } { 409 } \langle 240,1600 \rangle$

Question 7

Find values for b such that the triangle has no solutions.  
A = 24°, a = 5

Accepted Answer

A) $b > \frac { 5 } { \sin 24 ^ { \circ } }$ B) $b \leq \frac { 5 } { \sin 24 ^ { \circ } }$ C) $b = \frac { 5 } { \sin 24 ^ { \circ } }$ D) $b \geq \frac { 5 } { \sin 24 ^ { \circ } }$ E) $b < \frac { 5 } { \sin 24 ^ { \circ } }$ A) $b > \frac { 5 } { \sin 24 ^ { \circ } }$ B) $b \leq \frac { 5 } { \sin 24 ^ { \circ } }$ C) $b = \frac { 5 } { \sin 24 ^ { \circ } }$ D) $b \geq \frac { 5 } { \sin 24 ^ { \circ } }$ E) $b < \frac { 5 } { \sin 24 ^ { \circ } }$

Question 8

Find the dot product of u and v. 
$\begin{array} { l } 
\mathbf { u } = 6 \mathbf { i } + 4 \mathbf { j } \
\mathbf { v } = 8 \mathbf { i } - 2 \mathbf { j }
\end{array}$

Accepted Answer

A) 36 
B) 40 
C) 44 
D) 42 
E) 38 
A) 36 
B) 40 
C) 44 
D) 42 
E) 38

Question 9

Use the Law of Sines to solve for B and C.Round your answer to two decimal places.  
A = 145°, a = 28, b = 8

Accepted Answer

A) B $\approx$ 0.18°, C $\approx$ 32.89° 
B) B $\approx$ 0.18°, C $\approx$ 39.82° 
C) B $\approx$  9.43°, C $\approx$ 25.57° 
D) B $\approx$  25.57°, C $\approx$  9.43° 
E) B $\approx$  39.82°, C $\approx$  0.18° 
A) B $\approx$ 0.18°, C $\approx$ 32.89° 
B) B $\approx$ 0.18°, C $\approx$ 39.82° 
C) B $\approx$  9.43°, C $\approx$ 25.57° 
D) B $\approx$  25.57°, C $\approx$  9.43° 
E) B $\approx$  39.82°, C $\approx$  0.18°

Question 10

Given a = 10, b = 14, and c = 9, use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places.   Figure not drawn to scale

Accepted Answer

A) 94.78° 
B) 80.44° 
C) 39.84° 
D) 45.38° 
E) 60.33° 
A) 94.78° 
B) 80.44° 
C) 39.84° 
D) 45.38° 
E) 60.33°

Question 11

Find the standard form of the complex number $6 \left( \cos 17 ^ { \circ } 26 ^ { \prime } + i \sin 17 ^ { \circ } 26 ^ { \prime } \right)$ .Round values to the nearest hundredth.

Accepted Answer

A) 5.99 + 0.78i 
B)  5.72 + 1.8i 
C)  4.06 + 2.76i 
D)  -4.06 - 2.76i 
E)  -5.72 - 1.8i 
A) 5.99 + 0.78i 
B)  5.72 + 1.8i 
C)  4.06 + 2.76i 
D)  -4.06 - 2.76i 
E)  -5.72 - 1.8i

Question 12

Given a = 12, b = 14, and c = 7, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places. ​

Accepted Answer

A) 80.44° 
B) 91.02° 
C) 58.98° 
D) 29.99° 
E) 60.33° 
A) 80.44° 
B) 91.02° 
C) 58.98° 
D) 29.99° 
E) 60.33°

Question 13

Perform the operation shown below and leave the result in trigonometric form. $\left[ 6 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right) \right] \left[ 8 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right) \right]$

Accepted Answer

A)  $14 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$ 
B)  $48 \left( \cos 76 ^ { \circ } + i \sin 76 ^ { \circ } \right)$ 
C)  $14 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ 
D)  $14 \left( \cos 8 ^ { \circ } + i \sin 8 ^ { \circ } \right)$ 
E)  $48 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$ 
A)  $14 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$ 
B)  $48 \left( \cos 76 ^ { \circ } + i \sin 76 ^ { \circ } \right)$ 
C)  $14 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ 
D)  $14 \left( \cos 8 ^ { \circ } + i \sin 8 ^ { \circ } \right)$ 
E)  $48 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$

Question 14

Find values for b such that the triangle has one solution.  
A = 24 °, a = 16.2

Accepted Answer

A)  $b > 16.2 , b > \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
B)  $b \leq 16.2 , b = \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
C)  $b \leq 16.2 , b \neq \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
D)  $b \geq 16.2 , b \geq \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
E)  $b \geq 16.2 , b = \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
A)  $b > 16.2 , b > \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
B)  $b \leq 16.2 , b = \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
C)  $b \leq 16.2 , b \neq \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
D)  $b \geq 16.2 , b \geq \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
E)  $b \geq 16.2 , b = \frac { 16.2 } { \sin 24 ^ { \circ } }$

Question 15

Represent the complex number graphically, and find the trigonometric form of the number.  
5 - 5i

Accepted Answer

A)    $5 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$ 
B)    $5 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$ 
C)     $\sqrt { 50 } \left( \cos \frac { \pi } { 4 } + \sin \frac { \pi } { 4 } \right)$ 
D)     $\sqrt { 50 } \left( \cos \frac { \pi } { 4 } - i \sin \frac { \pi } { 4 } \right)$ 
E)     $\sqrt { 2 } \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
A)    $5 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$ 
B)    $5 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$ 
C)     $\sqrt { 50 } \left( \cos \frac { \pi } { 4 } + \sin \frac { \pi } { 4 } \right)$ 
D)     $\sqrt { 50 } \left( \cos \frac { \pi } { 4 } - i \sin \frac { \pi } { 4 } \right)$ 
E)     $\sqrt { 2 } \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$

Question 16

To approximate the length of a marsh, a surveyor walks 255 meters from point A to point B, then turns 81° and walks 225 meters to point C (see figure).Approximate the length AC of the marsh.     
Where a = 225 m, b = 255 m

Accepted Answer

A) 365.5 m 
B) 359.5 m 
C) 370.5 m 
D) 371.5 m 
E) 360.5 m 
A) 365.5 m 
B) 359.5 m 
C) 370.5 m 
D) 371.5 m 
E) 360.5 m

Question 17

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.   $2 \left( \cos 154 ^ { \circ } + i \sin 154 ^ { \circ } \right)$

Accepted Answer

A) 0.8767-1.7976i 
B) -1.7976  - 0.8767i 
C)  -1.7976 + 0.8767i 
D)  -0.8767-1.7976i 
E) None of the above 
A) 0.8767-1.7976i 
B) -1.7976  - 0.8767i 
C)  -1.7976 + 0.8767i 
D)  -0.8767-1.7976i 
E) None of the above

Question 18

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places.  
A = $\frac { 1 } { 2 }$ , b = $\frac { 2 } { 3 }$ , c = $\frac { 1 } { 3 }$

Accepted Answer

A) 0.08 
B) 0.10 
C) 0.12 
D) 0.06 
E) 0.11 
A) 0.08 
B) 0.10 
C) 0.12 
D) 0.06 
E) 0.11

Question 19

Perform the operation and leave the result in trigonometric form.   $\frac { \cos \pi + i \sin \pi } { \cos ( \pi / 9 ) + i \sin ( \pi / 9 ) }$

Accepted Answer

A)  $\cos \frac { 9 \pi } { 8 } - i \sin \frac { 9 \pi } { 8 }$ 
B)   $\cos \frac { 9 \pi } { 8 } - \sin \frac { 9 \pi } { 8 }$ 
C)  $\cos \frac { 8 \pi } { 9 } + i \sin \frac { 8 \pi } { 9 }$ 
D)   $\cos \frac { 8 \pi } { 9 } - i \sin \frac { 8 \pi } { 9 }$ 
E)   $\cos \frac { 9 \pi } { 8 } + i \sin \frac { 9 \pi } { 8 }$ 
A)  $\cos \frac { 9 \pi } { 8 } - i \sin \frac { 9 \pi } { 8 }$ 
B)   $\cos \frac { 9 \pi } { 8 } - \sin \frac { 9 \pi } { 8 }$ 
C)  $\cos \frac { 8 \pi } { 9 } + i \sin \frac { 8 \pi } { 9 }$ 
D)   $\cos \frac { 8 \pi } { 9 } - i \sin \frac { 8 \pi } { 9 }$ 
E)   $\cos \frac { 9 \pi } { 8 } + i \sin \frac { 9 \pi } { 8 }$

Question 20

Represent the complex number graphically, and find the trigonometric form of the number. 
 $6 + 6 i$

Accepted Answer

A)    $6 \sqrt { 2 }$ $\left( \cos \frac { \pi } { 4 } + \sin \frac { \pi } { 4 } \right)$ 
B)     $\sqrt { 6 }$ $\left( \cos \frac { \pi } { 4 } - i \sin \frac { \pi } { 4 } \right)$ 
C)    $\sqrt { 6 }$ $\left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
D)     $6 \sqrt { 2 }$ $\left( \cos \frac { \pi } { 4 } - i \sin \frac { \pi } { 4 } \right)$ 
E)     $6 \sqrt { 2 }$ $\left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
A)    $6 \sqrt { 2 }$ $\left( \cos \frac { \pi } { 4 } + \sin \frac { \pi } { 4 } \right)$ 
B)     $\sqrt { 6 }$ $\left( \cos \frac { \pi } { 4 } - i \sin \frac { \pi } { 4 } \right)$ 
C)    $\sqrt { 6 }$ $\left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
D)     $6 \sqrt { 2 }$ $\left( \cos \frac { \pi } { 4 } - i \sin \frac { \pi } { 4 } \right)$ 
E)     $6 \sqrt { 2 }$ $\left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$

Use the dot product to find the magnitude of u if $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 78.2, b = 52, c = 52

Multiply the complex numbers below and leave the result in trigonometric form. $\left[ 8 \left( \cos \frac { 2 \pi } { 7 } + i \sin \frac { 2 \pi } { 7 } \right) \right] \left[ 10 \left( \cos \frac { 5 \pi } { 9 } + i \sin \frac { 5 \pi } { 9 } \right) \right]$

Find the standard form of the complex number shown below. $5 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$

Plot the complex number 2.

Find the projection of u onto v. =\langle0,4\rangle =\langle3,20\rangle

Find values for b such that the triangle has no solutions. A = 24°, a = 5

Find the dot product of u and v. =6+4 =8-2

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. A = 145°, a = 28, b = 8

Given a = 10, b = 14, and c = 9, use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places. Figure not drawn to scale

Find the standard form of the complex number $6 \left( \cos 17 ^ { \circ } 26 ^ { \prime } + i \sin 17 ^ { \circ } 26 ^ { \prime } \right)$ .Round values to the nearest hundredth.

Given a = 12, b = 14, and c = 7, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places.

Perform the operation shown below and leave the result in trigonometric form. $\left[ 6 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right) \right] \left[ 8 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right) \right]$

Find values for b such that the triangle has one solution. A = 24 °, a = 16.2

Represent the complex number graphically, and find the trigonometric form of the number. 5 - 5i

To approximate the length of a marsh, a surveyor walks 255 meters from point A to point B, then turns 81° and walks 225 meters to point C (see figure).Approximate the length AC of the marsh. Where a = 225 m, b = 255 m

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $2 \left( \cos 154 ^ { \circ } + i \sin 154 ^ { \circ } \right)$

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = $\frac { 1 } { 2 }$ , b = $\frac { 2 } { 3 }$ , c = $\frac { 1 } { 3 }$

Perform the operation and leave the result in trigonometric form. $\frac { \cos \pi + i \sin \pi } { \cos ( \pi / 9 ) + i \sin ( \pi / 9 ) }$

Represent the complex number graphically, and find the trigonometric form of the number. $6 + 6 i$

Functions and Their Graphs

Polynomial and Rational Functions

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Exam 6: Additional Topics In Trigonometery

Use the dot product to find the magnitude of u if u=−3i+6j\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }u=−3i+6j

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​ A = 78.2, b = 52, c = 52 ​

Find the standard form of the complex number shown below. 5(cos⁡11π6+isin⁡11π6)5 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)5(cos611π​+isin611π​)

Plot the complex number 2. ​

Find the projection of u onto v. =\langle0,4\rangle =\langle3,20\rangle

Find values for b such that the triangle has no solutions. A = 24°, a = 5

Find the dot product of u and v. =6+4 =8-2

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. A = 145°, a = 28, b = 8

Given a = 10, b = 14, and c = 9, use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places. Figure not drawn to scale

Find the standard form of the complex number 6(cos⁡17∘26′+isin⁡17∘26′)6 \left( \cos 17 ^ { \circ } 26 ^ { \prime } + i \sin 17 ^ { \circ } 26 ^ { \prime } \right)6(cos17∘26′+isin17∘26′) .Round values to the nearest hundredth.

Given a = 12, b = 14, and c = 7, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places. ​

Find values for b such that the triangle has one solution. A = 24 °, a = 16.2

Represent the complex number graphically, and find the trigonometric form of the number. 5 - 5i

To approximate the length of a marsh, a surveyor walks 255 meters from point A to point B, then turns 81° and walks 225 meters to point C (see figure).Approximate the length AC of the marsh. Where a = 225 m, b = 255 m

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. 2(cos⁡154∘+isin⁡154∘)2 \left( \cos 154 ^ { \circ } + i \sin 154 ^ { \circ } \right)2(cos154∘+isin154∘)

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 12\frac { 1 } { 2 }21​ , b = 23\frac { 2 } { 3 }32​ , c = 13\frac { 1 } { 3 }31​

Perform the operation and leave the result in trigonometric form. cos⁡π+isin⁡πcos⁡(π/9)+isin⁡(π/9)\frac { \cos \pi + i \sin \pi } { \cos ( \pi / 9 ) + i \sin ( \pi / 9 ) }cos(π/9)+isin(π/9)cosπ+isinπ​

Represent the complex number graphically, and find the trigonometric form of the number. 6+6i6 + 6 i6+6i

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Use the dot product to find the magnitude of u if $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 78.2, b = 52, c = 52

Find the standard form of the complex number shown below. $5 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$

Plot the complex number 2.

Find the standard form of the complex number $6 \left( \cos 17 ^ { \circ } 26 ^ { \prime } + i \sin 17 ^ { \circ } 26 ^ { \prime } \right)$ .Round values to the nearest hundredth.

Given a = 12, b = 14, and c = 7, use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places.

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $2 \left( \cos 154 ^ { \circ } + i \sin 154 ^ { \circ } \right)$

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = $\frac { 1 } { 2 }$ , b = $\frac { 2 } { 3 }$ , c = $\frac { 1 } { 3 }$

Perform the operation and leave the result in trigonometric form. $\frac { \cos \pi + i \sin \pi } { \cos ( \pi / 9 ) + i \sin ( \pi / 9 ) }$

Represent the complex number graphically, and find the trigonometric form of the number. $6 + 6 i$