At Melior Games, when we create immersive gaming experiences, what often appears to be magic on screen is math in action. A small amount of sine, cosine, and tangent are silently at work behind every projectile’s smooth arc, every turret that spins, and every AI character who moves across a gaming area. Let’s take a closer look at how trigonometry influences the games we like making.
What is trigonometry, and why is it important to game developers?
Trigonometry is the branch of mathematics that studies the relationships between angles and sides of triangles. In game development, it’s one of the most practical tools, no exaggeration.
Why? Because games are full of motion, angles, and rotations, this is where trigonometry shines.
1. Character Rotation and Aiming
In many 2D and 3D games, we need characters or objects to rotate smoothly toward a point—an enemy, a mouse cursor, or a waypoint.
For example, in a top-down shooter, if you want the player character to rotate and aim at the mouse, you calculate the angle between the character and the cursor using the arctangent function.
float angle = Mathf.Atan2(targetY - originY, targetX - originX) * Mathf.Rad2Deg;
This angle is then applied to the rotation of the character, allowing for precise aiming.
2. Projectile Motion and Bullet Trajectories
Trigonometry is crucial whether you’re shooting an arrow, setting off a fireball, or figuring out the arc of a grenade.
Using sine and cosine, we can break down the launch angle and velocity into X and Y components.
float velocityX = Mathf.Cos(angleInRadians) * speed;
float velocityY = Mathf.Sin(angleInRadians) * speed;
This enables the trajectory to take on a natural arc, simulating genuine motion even in the presence of gravity.
3. Circular Motion and Orbits
Many enemy movement patterns, especially in bullet shooters, rely on circular motion. Trigonometric functions are ideal for positioning objects along a circle.
Let’s say you want an object to rotate around a point.
x = centerX + Mathf.Cos(angle) * radius;
y = centerY + Mathf.Sin(angle) * radius;
By increasing the angle in each frame, the object describes a perfect circle.
This is how rotating barriers, clock hands, and planetary orbits are modelled.
4. Field of View (FOV) and Cones of Vision
In stealth and strategy games, evaluating the angles of vectors is necessary to determine whether a character is visible to an adversary. This uses a dot product in conjunction with trigonometric functions to find the angle between directions.
float angle = Mathf.Acos(Vector3.Dot(directionToPlayer.normalized, enemyForward)) * Mathf.Rad2Deg;
We can determine that the player is in the field of view if this angle falls inside a specific threshold.
5. Lighting and Shadows
While this gets into more complex math, real-time lighting, especially in 2D engines like Unity’s Universal Render Pipeline (URP), can use trigonometric calculations to cast and animate shadows, simulate dynamic light falloff, and create soft light cones.
Why Trigonometry Matters at Melior Games
At Melior Games, we develop a variety of games for different platforms—from mobile to console—and many of them require systems built on these trigonometric foundations. Trigonometry is frequently used to ensure that everything runs smoothly while we’re modelling space physics, devising opponent behaviour, or developing novel weapon systems.
By understanding the math behind the scenes, we don’t just code—we create gameplay that feels fluid, responsive, and real. Trigonometry helps us hide complexity from the player while maintaining full control as designers.
Final Thoughts
Although game development is an art form, it has strong scientific roots, and one of its unsung heroes is trigonometry. Learning arithmetic will help you be more creative and create new gameplay options, regardless of your level of experience as a developer or designer.
Trigonometry is viewed as a potent tool in our creative toolbox at Melior Games rather than as an academic duty.
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