Finds the inverse of a function and gives it back as a power series. Feed it sin(x) and you get arcsin(x) written out as a series.
By Nick Orbeck. Original release page
How to install it
- Download the program with the button above. You'll get a .tns file, the file type TI-Nspire calculators use.
- Open nspireconnect.ti.com in Chrome on a computer or Chromebook, and plug your calculator in with its charging cable.
- Choose File Transfer, then To Calculator, then From Computer, and pick the .tns file you just downloaded.
- When it lands, the calculator shows a prompt. Choose Open to jump straight into it.
It sits in My Documents afterwards, so you can reopen it any time.
TI's web app only supports the CX II and CX II CAS. If you have an original CX, or you already use the TI-Nspire Student Software, sending the file through that works the same.
Running it
Open the document and go to its calculator page, then call invert with two things: the function you want inverted, and how many terms of the series to work out. invert(5x, 2) returns y/5, which is the inverse of y = 5x rearranged.
Answers come back in terms of y, not x, which is the right way round: you are asking what x was, given the y that came out.
Why a series
Most functions have no inverse you can write down in closed form. Swapping x and y and solving for y, the method from algebra class, runs out quickly outside textbook examples. A series is the workable answer: accurate near the point it is expanded around, and more so the more terms you ask for. Kepler's equation, which famously resists being rearranged, is the classic case and this handles it.