Polar Graphs Day 2 - by Wes Tully

We did two polar graphs today. One that had x and y axis symmetry. Which also means that if it is symmetrical to the x and y axis then it must be symmetrical to the origin. The other graph had 'maybe' symmetrical to the x and y axis.

r=4cos(2ϴ)

x-axis symmetry? Yes

r=4cos(2·-ϴ)

r=4cos(2ϴ)

y-axis symmetry? Yes

r=4cos(2(π-ϴ))☞r=4cos(2π-2ϴ)=☟

=4(cosπ2‧cosϴ2+sinπ2‧sinϴ2)= 4cos(2ϴ)

Origin? YES

Max r=4

ϴ	r
0	4
π/12	3.46
π/6	2
π/4	0
π/3	-2
5π/12	-3.46
π/2	-4

r=6sin(2ϴ)

x-axis? Maybe

y-axis? Maybe

r=6sin2(π-ϴ))=☟

=6sin(2π-2ϴ)=☟

=6(sin2π‧cos2ϴ-cosπ2‧sinϴ2)=☟

=-6sin(2ϴ)

Origin? Maybe

Max r=6

ϴ	r
0	0
π/6	5.2
π/4	6
π/3	5.2
π/2	0
11π/6	-5.2
5π/3	-5.2
3π/2	0
7π/4	-6

Rose Conjecture

Y=Acos(Bϴ)

Increasing a makes petals bigger and increasing b changes the number of petals.

Polar Graphs Day 1

What we did in class is learn how to graph polar equations. There are a few identities that are helpful to use for graphing the equations, they are: cos(-x)=cos(x) sin(-x)=-sin(x) sin(a-b)=sin(a)cos(b)-sin(b)cos(a) cos(a-b)=cos(a)cos(b)+sin(a)sin(b)

Before graphing you must test for symmetry. To test for x-axis symmetry (polar axis) you plug in (r,-x) to test for y-axis symmetry ( axis) you plug in (r, pi-x ) and to test origin symmetry (pole) you plug in (-r,x) and for all of these if you get the same equation you started with there is symmetry if you don't then you MIGHT have symmetry

Examples:

r=2-2sin(x)

Tests

polar axis:

r=2-2sin(-x)

r=2+2sin(x) (maybe)

y-axis:

(yes)

Origin:

-r=2-2sin(x) (maybe)

Example 2:

Polar axis:

(yes)

y-axis:

(Maybe)

Origin:

-r=2-cos(x)

Maybe















If you need more help go to mr. corn's website and the notes are on here.

Polar equation graphing!

codebase="http://www.geogebra.org/webstart/3.2/"
width="822" height="675" MAYSCRIPT>


















Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

if you need more help

if you need more help go to http://web.mac.com/jeffcorn/iWeb/Mr.%20Corn%27s%20Math%20Page/Precalculus.html

precalculus polar coordinate day 2 4/13

polar coordinate day 2 4/13
convert rectangular to polar

Using these equations

Try to get r or r^2 by itself

polar equations look like this

r=4

Solve this

So next thing you do is factor

Then divide both sides by the equation in parenthesesso you get

Now convert polar to rectangular

use equations

--->

well, the tangent of pie over 4 is 1, so xover y is one.

get the inverse which is


multiply by inverse sin to gte this

so y=3

Precalculus 4/12/2010

Polar coordinates - day 1

Formulas:

Example #1

finding polar coordinates

Find another part that r is negative:

Theta has to be greater than pi, and less than 2pi.

In order for that to happen you need to make the radius negative

when r is positive:

Theta has to be greater than -2pi and less than zero.

so you need to make theta negative for this one to work.

Example #2

Convert from Polar to Rectangular

use the equations given earlier

and the cosine of pi/2 is 0 so...

next you find y.

and the sine of pi/2 is 1 so...

So the point in rectangular form is (0,4)

Example #3

Converting from Rectangular to Polar

use the formulas provided above

Convert the point (-1,1)

Find r:

Find theta:

so you are left with the point:

If you need more help you can go to Mr.Corn's website: http://web.mac.com/jeffcorn/iweb

Thursday April 8, 2010

Trig Day 2

Example #1:

first you want to subtract a sine from both sides

next you want to divide both sides by two and then take the inverse sin of both sides

The equations that produce answers for this are

Example # 2

Make sure you find ALL solutions, not just going once around the unit circle.

Solution

Notice that it is only 1 pi instead of 2 THIS IS FOR TANGENT ONLY