Graph polar equations
Draw curves given as r in terms of θ, such as the three-petal rose r = 2 sin(3θ).
In polar form, each point is a distance r at an angle θ from the origin. The curve r = 2 sin(3θ) makes a rose with three petals, each up to 2 units long.
Use radians for polar graphs unless you have a reason to use degrees.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Open the mode screen. Move down to the graph-type row and move right twice to POL. Press enter, then leave the mode screen.
mode▼▼▼▶▶enter2ndQUITmodePress y= and type 2 sin(3θ). The θ is the X,T,θ,n key.
y=2sin3X,T,θ,n)Press zoom then 5 for a square window and graph. Then trace, and type π ÷ 6 to jump to θ = 30 degrees.
zoom5trace2ndπ^÷6enter
You should seer1=2sin(3θ) X=1.732050808Y=1
Natural Color Graphing
Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.
Open the Graph app. Press F3 (TYPE), then F2 for polar r=.
MENU3F3F2Type 2 sin(3θ) using the X,θ,T key for θ. Press EXE.
2sin3X,θ,T)EXEPress F6 to draw and F1 to trace, then the right arrow three times.
F6F1▶▶▶
You should seer1=2sin(3θ) θ=0.1884955592 r=1.07165359
Classic CAS
Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.
Go to the graphs page with doc. Open the menu, choose 5, Graph Type, then 3, Polar.
docmenu53Type 2 sin(3θ), using the θ key, and press enter. Then step the cursor along the curve with the right arrow.
2sin3θ)enter▶▶▶
You should seer1(θ)=2·sin(3·θ) x=1.70711 y=0.707107
Tips
- Try r = 1 + cos(θ) for a heart-like shape (a cardioid) and r = 2 for a plain circle.
- The graph repeats after θ goes from 0 to 2π. Set θmax to 2π (6.283) to see the whole curve.