Angle conversion is a basic calculation required in various fields:
Mathematics and Trigonometric Calculations
In calculating trigonometric functions (sin, cos, tan), most calculators and functions use the unit radian. Even if you understand angles in degrees, a conversion to radians is necessary for the calculation. For example, to calculate sin(90°), it is calculated as sin(π/2) = sin(1.5708 rad).
Physics and Rotational Motion
In physics, the radian is the standard unit when dealing with angular velocity and angular acceleration. For example, the angular velocity of an object rotating 60 times per second is 2π × 60 = 377 rad/s. Radians are also necessary for calculating the arc length in a circular motion s = rθ (r: radius, θ: radian).
Engineering and CAD Design
In architectural and mechanical design, it is common to express angles on drawings in degrees, but in surveying and some engineering fields, the gradian (400-division) is used. The gradian expresses a right angle as 100 gon and is characterized by a high affinity with the decimal system.
Programming and Graphics
In programming languages such as JavaScript and Python, trigonometric functions such as Math.sin() and Math.cos() expect radians. In CSS Transforms, degrees (deg) and turns (turn) can also be used, where rotate(0.25turn) means a 90-degree rotation.
Navigation and Surveying
In navigation and surveying, directions are expressed in 360 degrees. However, some surveying systems use the gradian (400 gon) to perform precise angle calculations. Radians are also used internally in GPS coordinate calculations.