Basic of Trigonometry for Game Development

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Basic Trigonometry:

Most of the contents here discussed, you have already done at your school level. So, if you already know everything, you can go forward to the next section. 

Apart from game development, Trigonometry is used in a number of fields ranging from physics, meteorology, astronomy, navigation, acoustics etc. 

We will start by learning about angles. An angle is nothing more than a figure that is created when two lines cross at a single point. The angles can be either represented in degrees or radians like 0°, 30°, 45°, 60° and 90°.

The sum of a triangle’s interior angles is 180 degrees. Similar to this, a quadrilateral’s internal angles all sum up to 360 degrees. The sum of a pentagon and a hexagon is 520 and 720 respectively.

Some of the terminology used for the angles are:

Acute Angle: Acute angles are those that are smaller than 90 degrees. 

Orthogonal Angle: A line is said to be perpendicular(also known as orthogonal) to another line when it crosses it at a 90° angle. Perpendicular lines may or may not touch each other but Orthogonal lines are perpendicular and touch each other at junction. So, we can call perpendicular as orthogonal. 

Typically, a little square box is drawn in the corner to represent this.

Obtuse angle: Obtuse angles are those that are greater than 90 degrees. 

Types of triangle based on angle:

  1. Acute angle triangle: When the angle between any 2 sides is less than 90 degrees it is called an acute angle triangle.
  2. Right angle triangle: When the angle between a pair of sides is equal to 90 degrees it is called a right-angle triangle.
  3. Obtuse angle triangle: When the angle between a pair of sides is greater than 90 degrees it is called an obtuse angle triangle.

Types of triangle based on sides of triangle: 

There are three basic types of triangles: scalene, right angled and isosceles.

A scalene triangle: When triangle has no sides of the same length.  

An isosceles triangle: When a triangle  has two sides of the same length.

  An Equilateral triangle: When a triangle has all three sides equal.

We will discuss more on the right Angle Triangles now because this is more important in game development.

Properties of Right Angle Triangles

In a right angled triangle, the longest side is called hypotenuse and it is the side opposite the right angle.

The sides that include the right angle are perpendicular and the base of the triangle.

According to pythagoras  theorem, 

Hypotenuse2 = Perpendicular2 + Base2

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