Guide to Game Development/Theory/Mathematics/Trigonometry/Degrees Vs Radians Vs Gradians

Degrees, radians and gradians are all different ways of measuring angles, and there isn't a standard, they all have their uses and so all of them are used. Degrees Degrees are denoted by the symbol: °. Degrees measure angles where a right-angle is 90°, this means that a line has an angle of 180° and that a circle has an angle of 360°. Radians Radians can be denoted by the symbol: r, but often no symbol is used. The greek letter pi (π) has been used as a constant of the ratio of a circle's circumference to its diameter. . Radians measure angles where a right-angle is , this means that a line has an angle of and that a circle has an angle of . As is a bit of a weird number for a full circle, the greek letter tau (τ) is often used to mean https://en.wikipedia.org/wiki/Tau#Mathematics. . The benefit of using this new constant is that now a right angle (a quarter of a circle) is , half of the circle is , three-quarters of a circle is and a full circle is . As this isn't the standard, throughout this book π will be used instead. Gradians Gradians are denoted by the symbol: g. Gradians are only used in continental Europehttps://en.wikipedia.org/wiki/Gradian. Gradians measure angles where a right-angle is 100g, this means that a line has an angle of 200g and that a circle has an angle of 400g. Converting between them Degrees Radians Gradians 1° 1.111...g 30° 33.333...g 45° 50g 60° 66.666...g 90° 100g 180° 200g 270° 300g 360° 400g References 75%