Desmos Graphing

Desmos Graphing

Polar Graphing: 
A system of coordinates in which the location of a point is determined by its distance from a fixed point at the center of the coordinate space (called the pole) and by the measurement of the angle formed by a fixed line (the polar axis, corresponding to the x-axis in Cartesian coordinates) and a line from the pole through the given point. The polar coordinates of a point are given as (r, θ), where r is the distance of the point from the pole, and θ is the measure of the angle.  (http://www.thefreedictionary.com/)

Equations to use: *must change graph type from Cartesian to Polar*

--Used to create "rose" shaped graphs--

• r= (a number)                                     
• r=acos(n*Theta)           
• r=asin(n*Theta) 
• r=asinbtheta

--Limacon --

•  r=a+bsin theta
• r=a+bcos theta

--Spiral of Archimedes--

•  r=theta

First Rose Shaped Graph

Steps:

1.    Go to www.desmos.com
2.    Change graph type to polar
3.    Put in equations
4.    r= (a number)
         --r= 0.5
5.    r=asin(n*Theta) 
         --r= 3 sin ( 4* theta)

Final Graph

Part 1:

Steps:

1.    Because all equations are known they can now be combined: multiplied/added/subtracted/divided.

2.    r= theta cos 6 + sin (8 theta) (8 sin 8 theta)

               -- r=acos(n*Theta)

               -- r=theta          

               -- r=asinbtheta

3.    r=88 (88 cos 8 theta) (8 sin 8 theta)

               -- r=a cos (n*Theta)

               -- r=theta

               -- r=a sin b theta

Part 2:

Equations Used:

1.    r=8 (sin 8 theta)   

           -- Orange center: r=asin(n*Theta)

                      --small rose graph

2.    r=88 (88 cos 8 theta) (8 sin 8 theta)

           -- star shaped center/ black lines: r=a cos (n*Theta), r=theta, r=a sin b theta

3.    r=6+(-5 (theta cos theta))

            -- green leaf: Limacon Graph, r=a+b cos theta

4.     r= -88 theta

            -- stem: Spiral of Archimedes with coefficient, r=theta

5.     r= theta cos 6 + sin (8 theta) (8 sin 8 theta)

            -- r=asinbtheta, r=theta, r=acos(n*Theta)

6.     r=100.02 sin 6 theta 

            -- Blue rose shaped graph: r=asinbtheta 

Loan Project

4% Interest Bank Loan 

4 Years: 5000                        A=5000(1+0.04)^4              A= 5849

3 Years: 5000                        A=5000(1+0.04)^3              A= 5624

2 Years: 5000                        A=5000(1+0.04)^2              A= 5408

   1 Years: 5000                        A=5000(1+0.04)^1              A= 5200   

_____________________________________________________________________________

    5849
    5624
    5408
 + 5200                                                                     
   22,081
                                                                          A=22081(1+0.04)^8           
                                                                          A=30219
                                                                                         

________________________________________________________________________________
                                                                          A=30219/96
                                                 
                                                                $ 314 per month for 8 years
_________________________________________________________________________________

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