Final Review Warm-up: p 58 – 60 #13, 21, 27, 37, 41, 49, 51, 55, 57, 61, 65

Unit 9: Chapter 9 The Polar Express In this unit we will answer… 9.1: graph in the polar coordinate system and use the corresponding distance formula (9-1, 9-2) 9.2: convert between polar and rectangular coordinates and equations (9-3) 9.3: simplify complex numbers (9-5) 9.4: perform operations on complex numbers in polar form (9-6, 9-7, 9-8)

9.1: graph in the polar coordinate system and use the corresponding distance formula (9-1, 9-2) In this section we will answer… What is the polar coordinate system? How do I write and graph points in polar form? How do I write and graph simple equations in polar form? Is there a way to find the distance between two points in polar form?

What is the polar coordinate system?

How do I write and graph points in polar form? Coordinate (r,θ) r = the distance from the pole to the point. θ = the angle. Plot some.

A few more in degrees…

Renaming points…

How do I write and graph simple equations in polar form? First, let’s look at one variable equations in rectangular. Graph x = 4 and y = -3

Now polar… r = 6 θ = -60 ˚

Is there a way to find the distance between two points in polar form?

Ta Da!!!

Find the distance…

Word Problem Surveying You are standing in the parking lot of a historical site reading the map of the area. You notice there is a monument 700 feet away and 40˚ to the left of your position and a gift shop 350 feet away and 35˚ to the right. How far is the monument from the gift shop?

Homework and Coming Events P 558 #17 – 49 every other odd

9.1: graph in the polar coordinate system and use the corresponding distance formula (9-1, 9-2) In this lesson we will answer… How are equations graphed in polar form? What are the basic families of graphs possible in polar form? How can I solve a system of polar equations?

Graph r = sin θ Use a T-chart. Connect points as you go so that you don’t mix them up. How does this differ from rectangular?

What do you expect it to look like? How do you think it will differ from r = sin θ? Graph it on your calculator.

You do NOT need to memorize these!

P 565 #11 – 27 odd – you may graph them on your calculators then sketch the result. Choose one polar equation from p 565 #11 – 22 to present on large polar graph paper. Must show a full, completed T-chart. Quiz Grade!

Warm-up: p #1 – 9 all, 17 - add respect to origin, 19, 21, 23, 33 – graph both function and inverse,

9.2: convert between polar and rectangular coordinates and equations (9-3) In this section we will answer… Can we convert from rectangular form to polar form and back again? How do I rename a polar point in rectangular form? A rectangular point in polar? How can I convert rectangular equations into polar form and visa versa?

Can we convert from rectangular form to polar form and back again?

How do I rename a polar point in rectangular form?

Do another.

How about this?

Now, name a rectangular point in polar.

How can I convert rectangular equations into polar form and visa versa?

A little harder…

One more…

Okay, now rectangular to polar…

Again…

Oooo…what about this? Have fun!

Homework: p 572 #15 – 39 odd Quiz tomorrow!!!

Warm-up: p 269 #15, 17, 21, 25, 35 – find # possible pos and neg roots, list all possible rational roots, then find the actual rational roots. 43 – use your calculators 45, 47, 51, 53, 57

Homework:

9.3: simplify complex numbers (9-5) In this section we will answer… Do I remember how to work with complex numbers? How do I rationalize with complex rational numbers?

What is a complex number?

Let’s review the powers of “i”:

Operations on Complex Numbers Addition and Subtraction Multiplication Division

Write an equation which has the solutions –2, 3+i, 3-i.

Homework: p 583 #13 – 35 odd

9.4: perform operations on complex numbers in polar form (9-6, 9-7, 9-8) In these sections we will answer… Can complex numbers be graphed? Is it possible to change a complex number into polar form? How do I get back to rectangular form fom polar? How do I multiply and divide complex numbers in polar form? Why on earth would anyone work in polar form?

Is it possible to change a complex number into polar form?

Polar Form of Complex Numbers

You do a couple…

How do I get back to rectangular form from polar?

You try one…

How do I multiply and divide complex numbers in polar form? First, let’s review the rules for multiplying bases with exponents.

The Product of Complex Numbers in Polar Form

Find the product then express the product in rectangular form.

Let’s review the rules for with dividing exponents.

Division of Complex Numbers in Polar Form

Find the quotient then express the quotient in rectangular form.

How do I raise complex numbers in polar form to a power or take a root? Review the rules for raising exponents to a power.

Powers and Roots of Complex Numbers in Polar Form

Find the power then express the result in rectangular form.

Why on earth would anyone work in polar form?

How about this? Doesn’t that look like fun?

Taking Roots of Complex Numbers. Don’t bother.

Change the root to a power and follow the power rule!

Homework: do one a day! P 590 #27 – 41 odd P 597 #11 – 25 odd P 605 #13 – 25 odd