Question 1

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations.
-

Accepted Answer

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

Question 2

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$\frac { 12 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right) } { 3 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right) }$

Accepted Answer

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

Question 3

Perform the indicated operations. Simplify the answer.
-$$\frac { \sqrt { - 175 } } { \sqrt { - 7 } }$$

Accepted Answer

A)  5 
B)  $- 5$ 
C)  $- 5 i$ 
D)  $5 \mathrm { i }$ 
A)  5 
B)  $- 5$ 
C)  $- 5 i$ 
D)  $5 \mathrm { i }$

Question 4

Find the product. Write the answer in standard form.
-$$( 4 + i ) ( - 4 - i )$$

Accepted Answer

A)  $- 17 - 8 \mathrm { i }$ 
B)  $- 15$ 
C)  $- 17$ 
D)  $- 15 - 8 \mathrm { i }$ 
A)  $- 17 - 8 \mathrm { i }$ 
B)  $- 15$ 
C)  $- 17$ 
D)  $- 15 - 8 \mathrm { i }$

Question 5

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 6 + 5 i } { 8 - 7 i }$$

Accepted Answer

A)  $\frac { 83 } { 113 } + \frac { 2 } { 113 } \mathrm { i }$ 
B)  $\frac { 13 } { 113 } + \frac { 82 } { 113 } \mathrm { i }$ 
C)  $\frac { 13 } { 15 }$ 
D)  $\frac { 83 } { 15 } - \frac { 82 } { 15 } \mathrm { i }$ 
A)  $\frac { 83 } { 113 } + \frac { 2 } { 113 } \mathrm { i }$ 
B)  $\frac { 13 } { 113 } + \frac { 82 } { 113 } \mathrm { i }$ 
C)  $\frac { 13 } { 15 }$ 
D)  $\frac { 83 } { 15 } - \frac { 82 } { 15 } \mathrm { i }$

Question 6

Find all cube roots of the complex number. Leave answers in trigonometric form.
-$64 \operatorname { cis } 120 ^ { \circ }$

Accepted Answer

A)  $4 \left( \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( - \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( \frac { \sqrt { 3 } } { 2 } - \frac { 1 } { 2 } \mathrm { i } \right)$ 
B)  $4 ( .7660 + .6428 \mathrm { i } ) , 4 ( - .9397 + .3420 \mathrm { i } ) , 4 ( .1736 - .9848 \mathrm { i } )$ 
C)  $4 \left( - \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) , 4 \left( \frac { 1 } { 2 } \mathrm { i } - \frac { \sqrt { 3 } } { 2 } \right) , 4 \left( \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right)$ 
D)  $4 ( .6428 + .7660 \mathrm { i } ) , 4 ( - .3420 + .9397 \mathrm { i } ) , 4 ( .9848 - .1736 \mathrm { i } )$ 
A)  $4 \left( \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( - \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( \frac { \sqrt { 3 } } { 2 } - \frac { 1 } { 2 } \mathrm { i } \right)$ 
B)  $4 ( .7660 + .6428 \mathrm { i } ) , 4 ( - .9397 + .3420 \mathrm { i } ) , 4 ( .1736 - .9848 \mathrm { i } )$ 
C)  $4 \left( - \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) , 4 \left( \frac { 1 } { 2 } \mathrm { i } - \frac { \sqrt { 3 } } { 2 } \right) , 4 \left( \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right)$ 
D)  $4 ( .6428 + .7660 \mathrm { i } ) , 4 ( - .3420 + .9397 \mathrm { i } ) , 4 ( .9848 - .1736 \mathrm { i } )$

Question 7

Determine two pairs of polar coordinates for the point with 0 $$0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$
-$( - 9,3 \sqrt { 3 } )$

Accepted Answer

A)  $\left( 6 \sqrt { 3 } , 150 ^ { \circ } \right) , \left( - 6 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
B)  $\left( 6 \sqrt { 3 } , 60 ^ { \circ } \right) , \left( - 6 \sqrt { 3 } , 300 ^ { \circ } \right)$ 
C)  $\left( 6 \sqrt { 3 } , 120 ^ { \circ } \right) , \left( - 9 \sqrt { 3 } , 240 ^ { \circ } \right)$ 
D)  $\left( 6 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 6 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
A)  $\left( 6 \sqrt { 3 } , 150 ^ { \circ } \right) , \left( - 6 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
B)  $\left( 6 \sqrt { 3 } , 60 ^ { \circ } \right) , \left( - 6 \sqrt { 3 } , 300 ^ { \circ } \right)$ 
C)  $\left( 6 \sqrt { 3 } , 120 ^ { \circ } \right) , \left( - 9 \sqrt { 3 } , 240 ^ { \circ } \right)$ 
D)  $\left( 6 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 6 \sqrt { 3 } , 330 ^ { \circ } \right)$

Question 8

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations.
-$$x = \sin t , y = \cos t ; t = \frac { \pi } { 2 }$$

Accepted Answer

A)  $( 1,0 )$ 
B)  $( 0 , - 1 )$ 
C)  $( - 1,0 )$ 
D)  $( , 1 )$ 
A)  $( 1,0 )$ 
B)  $( 0 , - 1 )$ 
C)  $( - 1,0 )$ 
D)  $( , 1 )$

Question 9

Indicate whether the statement is true always, sometimes, or never.
-The sum of two imaginary numbers is an imaginary number.

Accepted Answer

A) Always 
B) Sometimes 
C) Never 
A) Always 
B) Sometimes 
C) Never

Question 10

Give the rectangular coordinates for the point.
-$\left( 3 , \frac { 2 \pi } { 3 } \right)$

Accepted Answer

A)  $\left( \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right)$ 
B)  $\left( - \frac { 3 } { 2 } , \frac { 3 } { 2 } \right)$ 
C)  $\left( - \frac { 3 } { 2 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$ 
D)  $\left( \frac { 3 \sqrt { 3 } } { 2 } , - \frac { 3 } { 2 } \right)$ 
A)  $\left( \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right)$ 
B)  $\left( - \frac { 3 } { 2 } , \frac { 3 } { 2 } \right)$ 
C)  $\left( - \frac { 3 } { 2 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$ 
D)  $\left( \frac { 3 \sqrt { 3 } } { 2 } , - \frac { 3 } { 2 } \right)$

Question 11

Find the polar coordinates of the point(s)of intersection of the given curves for 0 $$0 \leq \theta < 2 \pi \text {. }$$
-$$\mathrm { r } = 3 + \cos \theta , \mathrm { r } = 3 - \sin \theta$$

Accepted Answer

A)  $\left( \frac { 5 } { 2 } , \frac { 3 \pi } { 4 } \right) , \left( \frac { 7 } { 2 } , \frac { 7 \pi } { 4 } \right)$ 
B)  $\left( 3 + \frac { 1 } { \sqrt { 2 } } , \frac { 3 \pi } { 4 } \right) , \left( 3 - \frac { 1 } { \sqrt { 2 } } , \frac { 7 \pi } { 4 } \right)$ 
C)  $\left( 3 , \frac { 3 \pi } { 4 } \right) , \left( 3 , \frac { 7 \pi } { 4 } \right)$ 
D)  $\left( 3 - \frac { 1 } { \sqrt { 2 } } , \frac { 3 \pi } { 4 } \right) , \left( 3 + \frac { 1 } { \sqrt { 2 } } , \frac { 7 \pi } { 4 } \right)$ 
A)  $\left( \frac { 5 } { 2 } , \frac { 3 \pi } { 4 } \right) , \left( \frac { 7 } { 2 } , \frac { 7 \pi } { 4 } \right)$ 
B)  $\left( 3 + \frac { 1 } { \sqrt { 2 } } , \frac { 3 \pi } { 4 } \right) , \left( 3 - \frac { 1 } { \sqrt { 2 } } , \frac { 7 \pi } { 4 } \right)$ 
C)  $\left( 3 , \frac { 3 \pi } { 4 } \right) , \left( 3 , \frac { 7 \pi } { 4 } \right)$ 
D)  $\left( 3 - \frac { 1 } { \sqrt { 2 } } , \frac { 3 \pi } { 4 } \right) , \left( 3 + \frac { 1 } { \sqrt { 2 } } , \frac { 7 \pi } { 4 } \right)$

Question 12

Provide an appropriate response.
-Which of the following pairs of parametric equations will graph a semicircle?

Accepted Answer

A)  $x = \cos \frac { 1 } { 4 } t , y = \sin \frac { 1 } { 4 } t , 0 \leq t \leq 4 \pi$ 
B)  $x = \cos \frac { 1 } { 2 } t , y = \sin \frac { 1 } { 2 } t , 0 \leq t \leq \pi$ 
C)  $x = \cos 2 t , y = \sin 2 t , 0 \leq t \leq \pi$ 
D)  $x = \cos t , y = \sin t , 0 \leq t \leq \frac { \pi } { 2 }$ 
A)  $x = \cos \frac { 1 } { 4 } t , y = \sin \frac { 1 } { 4 } t , 0 \leq t \leq 4 \pi$ 
B)  $x = \cos \frac { 1 } { 2 } t , y = \sin \frac { 1 } { 2 } t , 0 \leq t \leq \pi$ 
C)  $x = \cos 2 t , y = \sin 2 t , 0 \leq t \leq \pi$ 
D)  $x = \cos t , y = \sin t , 0 \leq t \leq \frac { \pi } { 2 }$

Question 13

Find the product. Write the answer in standard form.
-$( \sqrt { 3 } + 6 i ) ( \sqrt { 3 } - 6 i )$

Accepted Answer

A)  $- 3$ 
B)  39 
C)  $3 - 36 \mathrm { i }$ 
D)  $3 + 36 \mathrm { i }$ 
A)  $- 3$ 
B)  39 
C)  $3 - 36 \mathrm { i }$ 
D)  $3 + 36 \mathrm { i }$

Question 14

Provide an appropriate response.
-A projectile is launched from the ground with an initial velocity of v0 feet per second at an
angle of ϴ° above the horizontal. Write parametric equations in terms of v0 and ϴ that
model the flight of the projectile. Explain how you would use these equations, for given
values of v0 and ϴ, to determine the horizontal distance traveled by the projectile.

Accepted Answer

@#LAT-DLM&
First, solve @#LAT-DLM& for @#LAT-DLM& to determi

Question 15

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations.
-

Accepted Answer

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

Question 16

Write the number as the product of a real number and i.
-$$\sqrt { - 16 }$$

Accepted Answer

A)  $- \mathrm { i } \sqrt { 16 }$ 
B)  $4 \sqrt { i }$ 
C)  $4 \mathrm { i }$ 
D)  $- 4 \mathrm { i }$ 
A)  $- \mathrm { i } \sqrt { 16 }$ 
B)  $4 \sqrt { i }$ 
C)  $4 \mathrm { i }$ 
D)  $- 4 \mathrm { i }$

Question 17

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }$$

Accepted Answer

A)  $\frac { 5 } { 2 } + \frac { 5 \sqrt { 3 } } { 2 } \mathrm { i }$ 
B)  $\frac { 4 } { 3 } + \frac { 4 \sqrt { 3 } } { 3 } \mathrm { i }$ 
C)  $1 + \sqrt { 3 } \mathrm { i }$ 
D)  $8 + 8 \sqrt { 3 } \mathrm { i }$ 
A)  $\frac { 5 } { 2 } + \frac { 5 \sqrt { 3 } } { 2 } \mathrm { i }$ 
B)  $\frac { 4 } { 3 } + \frac { 4 \sqrt { 3 } } { 3 } \mathrm { i }$ 
C)  $1 + \sqrt { 3 } \mathrm { i }$ 
D)  $8 + 8 \sqrt { 3 } \mathrm { i }$

Question 18

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations.
-$$x = \sin t , y = \cos t ; t = \frac { \pi } { 3 }$$

Accepted Answer

A)  $\left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ 
C)  $\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ 
D)  $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ 
A)  $\left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ 
C)  $\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ 
D)  $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$

Question 19

Find the polar coordinates of the point(s)of intersection of the given curves for 0 $$0 < \theta < 2 \pi .$$
-$$\mathrm { r } = 6 \cos \theta , \mathrm { r } = - 1 + 4 \cos \theta$$

Accepted Answer

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

Question 20

Perform the indicated operation. Write the result in standard form.
-$$( + 4 i ) - ( + 5 i ) + ( 8 + 8 i )$$

Accepted Answer

A)  $17 + 17 \mathrm { i }$ 
B)  $+ 17 i$ 
C)  $+ 7 i$ 
D)  $- 15 - 9 i$ 
A)  $17 + 17 \mathrm { i }$ 
B)  $+ 17 i$ 
C)  $+ 7 i$ 
D)  $- 15 - 9 i$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. -

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 12 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right) } { 3 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right) }$

Perform the indicated operations. Simplify the answer. - $\frac { \sqrt { - 175 } } { \sqrt { - 7 } }$

Find the product. Write the answer in standard form. - $( 4 + i ) ( - 4 - i )$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 6 + 5 i } { 8 - 7 i }$

Find all cube roots of the complex number. Leave answers in trigonometric form. - $64 \operatorname { cis } 120 ^ { \circ }$

Determine two pairs of polar coordinates for the point with 0 $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( - 9,3 \sqrt { 3 } )$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \frac { \pi } { 2 }$

Indicate whether the statement is true always, sometimes, or never. -The sum of two imaginary numbers is an imaginary number.

Give the rectangular coordinates for the point. - $\left( 3 , \frac { 2 \pi } { 3 } \right)$

Find the polar coordinates of the point(s)of intersection of the given curves for 0 $0 \leq \theta < 2 \pi \text {. }$ - $\mathrm { r } = 3 + \cos \theta , \mathrm { r } = 3 - \sin \theta$

Provide an appropriate response. -Which of the following pairs of parametric equations will graph a semicircle?

Find the product. Write the answer in standard form. - $( \sqrt { 3 } + 6 i ) ( \sqrt { 3 } - 6 i )$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. -

Write the number as the product of a real number and i. - $\sqrt { - 16 }$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \frac { \pi } { 3 }$

Find the polar coordinates of the point(s)of intersection of the given curves for 0 $0 < \theta < 2 \pi .$ - $\mathrm { r } = 6 \cos \theta , \mathrm { r } = - 1 + 4 \cos \theta$

Perform the indicated operation. Write the result in standard form. - $( + 4 i ) - ( + 5 i ) + ( 8 + 8 i )$

Trigonometric Functions

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Filters

Exam 8: Complex Numbers, Polar Equations, and Parametric Equations

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. -

Perform the indicated operations. Simplify the answer. - −175−7\frac { \sqrt { - 175 } } { \sqrt { - 7 } }−7​−175​​

Find the product. Write the answer in standard form. - (4+i)(−4−i)( 4 + i ) ( - 4 - i )(4+i)(−4−i)

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - 6+5i8−7i\frac { 6 + 5 i } { 8 - 7 i }8−7i6+5i​

Find all cube roots of the complex number. Leave answers in trigonometric form. - 64cis⁡120∘64 \operatorname { cis } 120 ^ { \circ }64cis120∘

Determine two pairs of polar coordinates for the point with 0 0∘≤θ<360∘0 ^ { \circ } \leq \theta < 360 ^ { \circ }0∘≤θ<360∘ - (−9,33)( - 9,3 \sqrt { 3 } )(−9,33​)

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - x=sin⁡t,y=cos⁡t;t=π2x = \sin t , y = \cos t ; t = \frac { \pi } { 2 }x=sint,y=cost;t=2π​

Indicate whether the statement is true always, sometimes, or never. -The sum of two imaginary numbers is an imaginary number.

Give the rectangular coordinates for the point. - (3,2π3)\left( 3 , \frac { 2 \pi } { 3 } \right)(3,32π​)

Find the polar coordinates of the point(s)of intersection of the given curves for 0 0≤θ<2π. 0 \leq \theta < 2 \pi \text {. }0≤θ<2π. - r=3+cos⁡θ,r=3−sin⁡θ\mathrm { r } = 3 + \cos \theta , \mathrm { r } = 3 - \sin \thetar=3+cosθ,r=3−sinθ

Provide an appropriate response. -Which of the following pairs of parametric equations will graph a semicircle?

Find the product. Write the answer in standard form. - (3+6i)(3−6i)( \sqrt { 3 } + 6 i ) ( \sqrt { 3 } - 6 i )(3​+6i)(3​−6i)

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. -

Write the number as the product of a real number and i. - −16\sqrt { - 16 }−16​

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - 8(cos⁡90+isin⁡90)3(cos⁡30+isin⁡30)\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }3(cos30+isin30)8(cos90+isin90)​

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - x=sin⁡t,y=cos⁡t;t=π3x = \sin t , y = \cos t ; t = \frac { \pi } { 3 }x=sint,y=cost;t=3π​

Find the polar coordinates of the point(s)of intersection of the given curves for 0 0<θ<2π.0 < \theta < 2 \pi .0<θ<2π. - r=6cos⁡θ,r=−1+4cos⁡θ\mathrm { r } = 6 \cos \theta , \mathrm { r } = - 1 + 4 \cos \thetar=6cosθ,r=−1+4cosθ

Perform the indicated operation. Write the result in standard form. - (+4i)−(+5i)+(8+8i)( + 4 i ) - ( + 5 i ) + ( 8 + 8 i )(+4i)−(+5i)+(8+8i)

Trigonometric Functions

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Filters

Perform the indicated operations. Simplify the answer. - $\frac { \sqrt { - 175 } } { \sqrt { - 7 } }$

Find the product. Write the answer in standard form. - $( 4 + i ) ( - 4 - i )$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 6 + 5 i } { 8 - 7 i }$

Find all cube roots of the complex number. Leave answers in trigonometric form. - $64 \operatorname { cis } 120 ^ { \circ }$

Determine two pairs of polar coordinates for the point with 0 $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( - 9,3 \sqrt { 3 } )$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \frac { \pi } { 2 }$

Give the rectangular coordinates for the point. - $\left( 3 , \frac { 2 \pi } { 3 } \right)$

Find the polar coordinates of the point(s)of intersection of the given curves for 0 $0 \leq \theta < 2 \pi \text {. }$ - $\mathrm { r } = 3 + \cos \theta , \mathrm { r } = 3 - \sin \theta$

Find the product. Write the answer in standard form. - $( \sqrt { 3 } + 6 i ) ( \sqrt { 3 } - 6 i )$

Write the number as the product of a real number and i. - $\sqrt { - 16 }$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 8 ( \cos 90 + i \sin 90 ) } { 3 ( \cos 30 + i \sin 30 ) }$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \frac { \pi } { 3 }$

Find the polar coordinates of the point(s)of intersection of the given curves for 0 $0 < \theta < 2 \pi .$ - $\mathrm { r } = 6 \cos \theta , \mathrm { r } = - 1 + 4 \cos \theta$

Perform the indicated operation. Write the result in standard form. - $( + 4 i ) - ( + 5 i ) + ( 8 + 8 i )$