Solution 34616: Inverse Cosine of the Tangent of -5p/4 on the TI-84 Plus C Silver Edition Graphing Calculator.
Why is the inverse cosine of tan(-5pi/4) returning a Domain Error message on the TI-84 Plus C Silver Edition?
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-84 Plus C Silver Edition 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 example to get the same result:
1) Input tan(-5*p/4) [STO->] A
arcos(A) yields the same error as arcos(tan(-5*p/4)).
Please Note: The arcos function is displayed as follows:
Degree mode will work because (-225) is an integer. The same kind of problem exists if the input is a general floating point.
Please see the TI-84 Plus C Silver Edition guidebook for additional information.