SOLUTION: So I tried calculating the Cotangent of {{{pi / 2}}} (90 degrees). The answer is 0, but my scientific calculator (Casio Fx300ES Plus) didn't say that. I inputted: ‍‍

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: So I tried calculating the Cotangent of {{{pi / 2}}} (90 degrees). The answer is 0, but my scientific calculator (Casio Fx300ES Plus) didn't say that. I inputted: ‍‍       Log On

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Question 1205097: So I tried calculating the Cotangent of pi+%2F+2 (90 degrees). The answer is 0, but my scientific calculator (Casio Fx300ES Plus) didn't say that.
I inputted:
‍‍ ‍‍ ‍
But I got a Math ERROR. The answer is 0, not undefined? Why's that?
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

cot%28pi%2F2%29=1%2Ftan%28pi%2F2%29
since tan%28pi%2F2%29=infinity, you have cot%28pi%2F2%29=1%2Finfinity
so you need to use identity tan%28pi%2F2%29=sin%28pi%2F2%29%2Fcos%28pi%2F2%29, then you have

cot%28pi%2F2%29=1%2F%28sin%28pi%2F2%29%2Fcos%28pi%2F2%29%29

cot%28+pi%2F2%29=cos%28pi%2F2%29%2Fsin%28pi%2F2%29.....since cos%28pi%2F2%29=0 and sin%28pi%2F2%29=1, you have

cot%28+pi%2F2%29=0%2F1
cot%28+pi%2F2%29=0


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

I'm not 100% certain if this is the case with Casio calculators, but check out this page here
https://stackoverflow.com/questions/345085/how-do-trigonometric-functions-work

The CORDIC algorithm can be used to compute cos(pi/2) and sin(pi/2)
Since pi/2 is a common angle, likely your calculator will retrieve the following from a lookup table.
cos(pi/2) = 0
sin(pi/2) = 1

Then under the hood your calculator would then use the identity that
cot = cos/sin
So you'll have 0 up top and 1 down below.
The ultimate result is 0. This is the correct value of cot(pi/2)

Why does your calculator throw an error when computing 1/tan?
Because tan = sin/cos, and cos(pi/2) = 0.
So tan(pi/2) = 1/0 = undefined
tan(pi/2) being undefined leads to the 1/tan also undefined (even though it should be 0).

Technically what's going on is that as x gets closer to pi/2 from the left, tan(x) approaches positive infinity.
Stuff of the form 1/tan will approach 0 because you have something like 1/(some really large number).
If you haven't covered limits yet then don't worry.