Arctan (or “inverse tangent”) is an important trigonometric function which is used to calculate the angle of a right triangle given the ratio of two sides. It can also be used to solve other types of equations involving angles and triangles. To find its value, it’s necessary to use a variety of mathematical methods including Taylor series expansions, numerical integration, and basic properties of trigonometry such as the identities for sine and cosine. Depending on the application or context in which Arctan needs to be calculated, different approaches may better suited than others. This essay will provide an overview of how Arctan works with focus on Taylor Series Expansion and numerical integration.

To start off, it’s important to have some understanding about what arctangent is exactly. The arctangent is defined as: “the angle whose tangent is equal to a given number” (Hatcher et al., 2019). In essence, this means that if we know the ratio between two sides in a right triangle (which we usually refer to as “opposite” over “adjacent”), then we can use the definition above in order to determine what size angle would make this ratio true. This concept lies at the core of many useful applications from navigation systems like GPS devices all the way up through computer graphics where it’s fundamental for modern game engines like Unity3D or Unreal Engine 4 (Fortescue et al., 2014).

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