Why does math.acos result in ValueError: math domain error?

Question

I am using math.acos() function :

math.acos(1.0000000000000002)

This throws a math domain error. Can someone tell the reason? I am getting this value calculated before and here this value gives error but if I remove 2 at the end it does not throw error. I did not get the reason to this.

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Asked By: shalki

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Source

Answer 1

You are trying to do acos of a number for which the acos does not exist.

Acos – Arccosine , which is the inverse of cosine function.

The value of input for acos range from -1 <= x <= 1 .

Hence, when trying to do math.acos(1.0000000000000002), you are getting the error.

If you try higher numbers, you will keep getting the same error – math.acos(2) leads to ValueError: math domain error

Answered By: Anand S Kumar

Answer 2

Inverse cosine is defined only between -1 and 1, inclusive. The arc-cosine of 1.0000000000000002 has no mathematical or semantic meaning other than “does not exist” or “undefined”.

Of course, since inverse cosine of 1 does exist, acos(1) doesn’t throw any error.

Answered By: nanofarad

Why does math.acos result in ValueError: math domain error?

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