Since we have a simple conversion method for converting from radians to degrees, 180/pi or vice versa, could we apply this to Euler's Identity, e^(i pi)=−1 and traditionally in radians, to produce an equation that is in degrees; one that may or may not be as simplistic or beautiful as the radian version, but yet is still quite mathematically true? If not, why? If so, how did you derive it?

Siena Erickson

Siena Erickson

Answered question

2022-11-12

Since we have a simple conversion method for converting from radians to degrees, 180 π or vice versa, could we apply this to Euler's Identity, e i π = 1 and traditionally in radians, to produce an equation that is in degrees; one that may or may not be as simplistic or beautiful as the radian version, but yet is still quite mathematically true?

If not, why? If so, how did you derive it?

Answer & Explanation

Taniyah Lin

Taniyah Lin

Beginner2022-11-13Added 14 answers

Given that
180 ° = π
we could write
e 180 ° i = 1
Jorge Schmitt

Jorge Schmitt

Beginner2022-11-14Added 5 answers

If your angles are in degrees,
e ˙ i 180 = 1 ,
where
e ˙ = e π / 180 = 1.0176064912058515755792228003847
is the constant of Euler-the-Fool.

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