Parametric & Polar Graphing on the TI-84 (Par & Pol Modes)
Ready to graph beyond y = f(x)? This parametric polar TI-84 guide shows you how to graph parametric equations in Par mode and polar equations in Pol mode: switch MODE, enter X1T/Y1T or r1, set the window, and TRACE along the curve.
Quick answer: Press MODE, arrow to Par or Pol, and press ENTER. In the Y= editor, type parametric equations as X1T and Y1T (the T key is X,T,θ,n) or a polar equation as r1. Set Tmin=0, Tmax=2π, Tstep=π/24 in WINDOW, press GRAPH, and use TRACE to move along the curve.
Switching to Parametric mode
- Press MODE.
- On the fourth line you will see Func Par Pol Seq. Arrow to Par and press ENTER to highlight it.
- Press 2ND + MODE (QUIT).
Now press Y=: instead of Y1=, Y2=, you see X1T=, Y1T=, X2T=, Y2T= — the calculator is ready for parametric input.
Entering and graphing parametric equations
Let us graph the circle x = 2cos(t), y = 2sin(t) — the classic parametric equation (see Wikipedia for the full theory):
- Press Y=. At X1T= type 2*cos(T) — get T from the X,T,θ,n key.
- At Y1T= type 2*sin(T).
- Press WINDOW and set Tmin=0, Tmax=2π (π is 2ND + ^), Tstep=π/24. Then set a square-friendly X/Y window, or simply press ZOOM → 5:ZSquare after graphing so the circle does not look like an oval.
- Press GRAPH.
Tstep controls smoothness: smaller values draw a smoother curve but take longer. π/24 is a good default. Practice on our free TI-84 calculator before your exam.
Switching to Polar mode and graphing r1
- Press MODE, highlight Pol, press ENTER, then 2ND + MODE (QUIT).
- Press Y= — you now see r1=, r2=, …
- At r1= type a polar equation, for example 2+2*cos(θ) (a cardioid). The θ comes from the X,T,θ,n key.
- Press WINDOW: set θmin=0, θmax=2π, θstep=π/24, plus sensible X/Y limits (try Xmin=−6, Xmax=6, Ymin=−4, Ymax=4).
- Press GRAPH.
For a full rose or spiral you may need θmax larger than 2π — some curves only close after 4π. If your graph looks incomplete, double θmax and graph again.
Using TRACE in Par and Pol modes
Press TRACE and use the arrow keys to walk along the curve. In Par mode the screen shows the current T value plus the X and Y coordinates at that point. In Pol mode it shows θ and the X/Y coordinates. Mastering TRACE is the key to the parametric polar TI-84 workflow.
Common pitfalls
- Forgetting to switch back to Func. The #1 beginner mistake. After parametric work, press MODE, highlight Func, and press ENTER — otherwise your normal Y= functions will not graph.
- Degree mode with trig. Parametric and polar equations using sin/cos need radians: MODE → Radian → ENTER.
- Tmax too small. A half-drawn curve usually means the parameter range does not cover the full period — raise Tmax/θmax.
More graphing walkthroughs live in our TI-84 guides hub. Bookmark this parametric polar TI-84 tutorial for exam season.
Parametric polar TI-84: frequently asked questions
Why is my circle showing as an oval?
Your viewing window is not square. Press ZOOM → 5:ZSquare right after graphing.
My normal Y= functions will not graph anymore. What happened?
You are still in Par or Pol mode. Press MODE, highlight Func, press ENTER.
Why does my graph look dotted or jagged?
Your Tstep (or θstep) is too large. Go to WINDOW and make the step smaller, e.g. π/48.
Can I graph two parametric curves at once?
Yes — enter the second curve as X2T= and Y2T= in the Y= editor and both draw together.
How do I switch back to normal function mode?
Press MODE, arrow to Func, and press ENTER. Your Y= functions will graph normally again — a must-know step in any parametric polar TI-84 session.
What is Tstep (or θstep) and why does it matter?
Tstep (or θstep) controls how finely the calculator samples the curve as the parameter changes. Smaller values draw smoother graphs but take longer to render. Start with π/24 and reduce it to π/48 if the curve looks dotted or jagged.
How do you graph parametric equations on a TI-84?
Press MODE, arrow to Par on the fourth line (Func Par Pol Seq), press ENTER, then press 2ND QUIT. Press Y= and type your equations at X1T= and Y1T=, getting T from the X,T,θ,n key — for example, X1T=2cos(T) and Y1T=2sin(T) draws a circle. Set Tmin=0, Tmax=2π and Tstep=π/24 in WINDOW, press GRAPH, and use ZOOM 5:ZSquare so the circle does not look like an oval.
How do you graph polar equations on a TI-84?
Press MODE, highlight Pol, press ENTER, then press 2ND QUIT. Press Y= and type your equation at r1=, getting θ from the X,T,θ,n key. Set θmin=0, θmax=2π and θstep=π/24 in WINDOW, with Xmin=−6, Xmax=6, Ymin=−4 and Ymax=4, then press GRAPH.
How do you switch a TI-84 to parametric (Par) mode?
Press MODE and find the fourth line, which shows Func Par Pol Seq. Arrow to Par, press ENTER to highlight it, then press 2ND QUIT to return to the home screen. The Y= editor will now show X1T= and Y1T=; remember to switch back to Func afterwards, or normal function graphs will not work.
How do you graph a cardioid or rose curve on a TI-84?
Switch to Pol mode, then type the equation at r1= — for example, r1=2+2cos(θ) draws a cardioid. Use θmin=0, θmax=2π and θstep=π/24 in WINDOW; a full rose or spiral may need θmax larger than 2π, since some curves only close after 4π. Press TRACE and use the arrow keys to walk along the curve and read θ with the X and Y values.
