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

Question 1

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

Answer 1

C

Question 2

Give the rectangular coordinates for the point.

Answer 2

C

Question 3

The graph of a polar equation is given. Select the polar equation for the graph

Answer 3

D

Question 4

Find the product. Write the answer in standard form.

Question 5

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

Question 6

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.

Question 7

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.

Question 8

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

Question 9

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

Question 10

The graph of a polar equation is given. Select the polar equation for the graph

Question 11

The graph of a polar equation is given. Select the polar equation for the graph.

Question 12

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

Question 13

The graph of r = a 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 to graph the spiral in the window specified.

Question 14

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

Question 15

Find a rectangular equation for the plane curve defined by the parametric equations.

Question 16

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.

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

Find the polar coordinates of the point(s)of intersection of the given curves for 0

Question 22

Find all cube roots of the complex number. Leave answers in trigonometric form.
-8

A)2 cis 30°, 2 cis 150°, 2 cis 270°
B)2 cis 180°, 2 cis 0°
C)2 cis 60°, 2 cis 180°, 2 cis 300°
D)2 cis 120°, 2 cis 180°, 2 cis 300°

Question 23

Write the number as the product of a real number and i.

Question 24

Find the product. Write the product in rectangular form, using exact values.

Question 25

Find the polar coordinates of the point(s)of intersection of the given curves for 0

Question 26

Solve the problem.
A projectile is fired with an initial velocity of 350 feet per second at an angle of 45° with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the
Nearest tenth of a second.)

A)23.6 sec
B)15.5 sec
C)20.3 sec
D)12.1 sec

Question 27

Find the given power. Write answer in rectangular form.

Question 28

Find sum of the pair of complex numbers.

Question 29

Solve the quadratic equation and express all nonreal complex solutions in terms of i.

Question 30

Find the quotient. Write the answer in standard form.

Question 31

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may

Question 32

Find all cube roots of the complex number. Leave answers in trigonometric form.

Question 33

Graph the cycloid for t in the indicated interval.

Question 34

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.

Question 35

Find the quotient. Write the answer in standard form.

Question 36

Solve the quadratic equation and express all nonreal complex solutions in terms of i.

Question 37

Find the product. Write the answer in standard form.

Question 38

Find an equivalent equation in rectangular coordinates.

Question 39

Determine two pairs of polar coordinates for the point with 0

Question 40

The rectangular coordinates of a point are given. Express the point in polar coordinates with

Question 41

Graph the polar equation for in [0°, 360°).

Question 42

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.

Question 43

Perform the indicated operations. Simplify the answer.

Question 44

Find the given power. Write answer in rectangular form.

Question 45

Find all specified roots.

Question 46

Perform the indicated operation. Write the result in standard form.

Question 47

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.

Question 48

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

Question 49

Find the product. Write the answer in standard form.

Question 50

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.

Question 51

Write the complex number in rectangular form.

Question 52

Find the product. Write the answer in standard form.

Question 53

Find the polar coordinates of the point(s)of intersection of the given curves for 0

Question 54

For the given rectangular equation, give its equivalent polar equation.

Question 55

Perform the indicated operation. Write the result in standard form.

Question 56

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

A)Always
B)Sometimes
C)Never

Question 57

Perform the indicated operations. Simplify the answer.

Question 58

Solve the problem.
A projectile is fired with an initial velocity of 400 feet per second at an angle of 70° with the horizontal. In how many seconds will the projectile reach its maximum altitude? (Round your
Answer to the nearest tenth of a second.)

A)16.6 sec
B)8.4 sec
C)11.8 sec
D)19.9 sec

Question 59

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.

Question 60

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.