Education Technology

# Knowledge Base

## Solution 12560: Inverse Cosine of the Tangent of -5p/4 on the TI-83 Family and TI-84 Plus Family.

### Why is the inverse cosine of tan(-5pi/4) returning an Domain Error message on the TI-83 family and TI-84 Plus family?

This is a classic problem with floating point arithmetic that is used in calculators and almost all computers.

The main problem is tan(-5*p/4). The TI-83 family and TI-84 Plus family only performs calculations with 14 digits in the memory, the calculation of tan (-5*p/4) loses some accuracy on the last digit. Internally, the answer of tan(-5*p/4) is not -1 but something like -1.0000000000001. The display routine on the calculator is designed to display -1 instead of the internal number. However, arcos function will take the internal number -1.0000000000001 as input and determines it is out-of-range.

Try the following to get the same result:

tan(-5*p/4) [STO->] A
arcos(A) yields the same error as arcos(tan(-5*p/4)).

Note: the arcos function is displayed as follows:

Degree mode works fine because (-225) is an integer. Same kind of problem exists if the input is a general floating point.

Please see the TI-83 family and TI-84 Plus family guidebooks for additional information.