How To Do Vector Calculations With Polar Coordinates On The TI-84 Plus CE Calculator

I would be absolutely lying if I told you that the polar coordinate functions of my beloved TI-84 Plus CE calculator were anything less than horribly annoying. Like a lot of math, and math calculators, there are roughly 3312 (that’s considered the “KM1NDY number”,i.e., K#, for those learning the most avant garde methods of mathematics) different ways to solve vector calculations. I just want one good one. I want to plug in a polar coordinate into my calculator add some math function (+, -, *, / , you know the drill…), plug in another polar coordinate, and get a result. Or, even better yet, mix and match rectangular and polar coordinates and have the calculator do its thing. But, alas, no such luck… And, to boot, internet sources on this topic…including Texas Instrument’s very own manual(!)…were not particularly helpful. Maybe I was tired, maybe I can’t read very well, maybe IT JUST DOESN’T WORK, maybe, who knows?

Regardless, after spending K# hours trying to resolve this, I finally got something to work…

Here is the problem we are trying to solve: 120<-220° x 95<200°

So, to start, the set-up in the MODE section of the TI-84 Plus CE is critical. Make sure to select “RADIAN“, “POLAR“, and then the polar form for imaginary numbers [ re^(ϴi) ].

Now, you can pretty much type in the polar coordinates of the vectors you are interested in doing calculations with. You do need to use a specific form as shown in the first line of the calculator below.

In considering the vector (in polar coordinates) 120<-220°, you simply:

1. Type in the magnitude as is (i.e., 220).
2. Then Euler’s number (that is “e^x “, which is found by punching the “2nd” key and then “ln“).
3. Then the angle (i.e., -220) with the i (found by punching the “2nd” key and then “.“) to indicate the imaginary component of the vector.
4. Then type in π/180 as part of the superscript of e. This is necessary, because in order for the TI-84 Plus CE to perform this operation, the angle of the vector must be in radians and not degrees. Recall that to convert degrees to radians, you need to multiple the degrees by π/180. So, -220 degrees is actually -3.84 radians [ i.e., -220 x (π/180) ].
5. Now type in your desired operator. In this case I chose multiplication (*).
6. And type in the next vector in polar coordinates using the same methodology.
7. Once you hit enter, you will return the correct magnitude (11400), but the angle is now in radians (-0.35i). And if this suits your purposes, then you are done!

I, however, wanted to have consistency, with my answer in degrees and not radians. This meant that I now needed to go into the calculator’s MODE tab in order to alter the set-up. Specifically, I needed to change the angle mode from RADIAN to DEGREE.

Once this was done, I could type the number of radians (i.e., -.35) into the next line of the calculator.

At this point, I can open the angle menu by hitting the 2nd key and then the apps key. Once in the angle menu, choose “r” for radians.

This will add the little superscript r after the radians you have entered into the calculator (i.e., -.35^r for this example). As long as you are now in DEGREE mode, you can simply hit enter, and the calculator will convert the radians to degrees for you.

So, in conclusion, 120<-220° x 95<200° equals 11400<-20°.

Like I said before, there #K ways to solve vector problems on the TI-84. But after quite a bit of time trying to figure out how to successfully input vectors in polar form and perform math on them, this was the best way that I found. There are of course umpteen ways to convert between polar and rectangular form as well, and, well, they are just as annoying.

Hope it helps! I expect, I will need to look at this blog to remember how to do it myself in the not so distant future.

KM1NDY