Chapter Sections 8.1-8.3

Question 0

What are polar coordinates?

Answer 0

P (r, theta)
r is the radius
Theta is the angle it is on in the unit circle

Question 1

What are two equations to know for converting from polar to rectangular?

Answer 1

r sin (theta) =y
r cos (theta) =x

Question 2

When converting from rectangular to polar what do you do?

Answer 2

First you use the Pythagorean theorem to find the radius

Then use tangent to find the degree

Question 3

To write an equation in rectangular coordinate what are your two options

Answer 3

• multiply both sides by r

- square both sides

Question 4

What is the equation for limaçon curves without an inner loop? And how do you know it is a limaçon curve without inner loop?

Answer 4

R=a+/- b cos theta

You know it is a limaçon curve without inner loop because a > b

Question 5

How many times does a limaçon curve without an inner loop pass through the origin?

Answer 5

It doesn’t pass through the origin

Question 6

What is the equation for a limaçon curve with an inner loop? And how do you know it is this type of curve?

Answer 6

R=a +/- b sin theta

You know it’s this equation because a

Question 7

How many times does a limaçon curve with inner loop cross the origin?

Answer 7

Twice

Question 8

What is the equation for a cardiod graph (there are two)?

How do you know it’s a cardiod graph?

Answer 8

R=a +/- a sin theta
R=a +/- a cos theta
You know it’s this graph because a will = b

Question 9

Cos is the value for y or x

Answer 9

For x

Question 10

Sin is the value for y or x

Answer 10

For y

Question 11

What makes something rectangular?

What makes something polar

Answer 11

When it has to do with x and y and i

When it has to do with theta and radius

Question 12

What is the general equation for a complex number?

Answer 12

A + bi

Question 13

When plotting a complex number where is the imaginary number with the i and where is the real number?

Answer 13

Imaginary number with i goes on y axis and real number goes with x axis

Question 14

What is the polar form of a complex number?

Answer 14

Z= r (cos theta + i sin theta)

Question 15

What is the equation for products of complex numbers

Answer 15

z1 * z2= r1*r2 (cos (theta1+theta2) + i sin(theta1+theta2))

Question 16

What is the equation for the quotient of complex numbers?

Answer 16

z1/z2= r1/r2 (cos (theta1-theta2) + i sin(theta1-theta2))

Question 17

What is the equation for a complex number to a certain power

Answer 17

Z^n=r^n (cos(n*theta) + i sin(n *theta))

Question 18

What is the equation for finding complex roots?

Answer 18

Zk=the Nth square root of r (cos(theta/n +360k/n) + i sin(theta/n + 360k/n))

Question 19

What would K be in the equation for finding the complex roots

Answer 19

K = n-1
For example)
If n is 3 then k would be 0,1,2 giving us three solutions

Question 20

What is known for the complex root of unity?

Answer 20

Unity means 1
So r = 1
Theta= 0 degrees

Question 21

What is the trick you can do when finding roots of unity

Answer 21

For each possible equation you can simply keep adding the number in front of the K. So if it is 90k then in the solutions it would be cos 0 the in the next possible solution it would be cos 90 etc

Question 22

REMEMBER!!!

Answer 22

If graphing state whether it is a circle (with its center and radius), if it is a vertical line, slanted line, or horizontal line.

Question 24

What are the points to test for a limaçon curve using sine in the equation such as 2-4sin

Answer 24

3pi/2
5pi/3
11pi/6
0
Pi/6
Pi/3
Pi/2

Question 25

What are the points to test for a limaçon curve using cos in its equation

Answer 25

0
Pi/6
Pi/3
Pi/2
2pi/3
5pi/6
Pi