How Radians Work

A radian is a unit of measure for angles similar to degrees. Technically speaking the only difference between the two is the conversion but radians are a useful measurement to remember for many reasons. 1: It is the standard unit of angular measure used across the world. 2: It is used in a relationship to find the radius, and arc length of a circle. 3: Some calculus and physics formulas require the radian and will not give the correct value if degrees are used.

To determine radians lets first compare it to a unit that people are more common with such as degrees. Radians are described in ∏ “pi” and ∏ = 180°; therefore the conversion from degrees to radians is (Degrees)* ∏/180° = (Radians); and vice versa would be (Radians)* 180°/∏ = (Degrees).

In mathematics radians are usually used in reference to circles. A complete circle has a total of 360° making it 2∏. 2 seems much simpler than 360 and this is why some people believe work should be done with radians; just because it is simpler to work with. Most of the time when working with radians you are working with a simple fraction or decimals which could lead to less calculation error on the operators behalf. Below I have listed the typical radian measures that appear most practice eqations.

Full Circle = 360° = 2∏
270° = 1.5∏
Semi-Circle = 180° = ∏
90° = 0.5∏
0° = 0∏

Now that we have a firm understanding of what radians we can figure out what are its applications. Radians are frequently used (much more often than degrees) in Trigonometry with trigonometric functions. Such functions are sine, cosine, tangent, cosine, secant, and cotangent. All of these functions have different mathematical values but they are used to find many things like the angles or sides of any right triangle.

Not only do radians have a strong appearance in mathematics but they also appear in many scientific formulas that involve angles. Some topics in physics are angular velocity, angular acceleration, trajectory, component vectors, and angular momentum. With this many topics involved with angles and radians one can determine that radians are quite a significant influence in the scientific field of physics.

Radians operate just like degrees; but since they look simpler and are more widely used they were picked as the standard unit for angle measure and is used in many equations. You simply plug in the radian value for θ “theta” in a given equation and solve for some variable or vice versa. Many people without working experience with radians tend to find them threatening at first but after working with them for a while you will realize that they are like any other variable and they are simple to work with.