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
- 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
