Mathematics for Game Development

6.

Trigonometry in Games

6.1.

Fundamental Trigonometric Functions

6.1.1.

6.1.1.1.

Unit Circle Interpretation

6.1.1.2.

Graph Properties

6.1.1.3.

Domain and Range

6.1.2.

Cosine Function

6.1.2.1.

Unit Circle Interpretation

6.1.2.2.

Graph Properties

6.1.2.3.

Domain and Range

6.1.3.

Tangent Function

6.1.3.1.

Relationship to Sine and Cosine

6.1.3.2.

Graph Properties

6.1.3.3.

Asymptotes and Discontinuities

6.1.4.

6.1.4.1.

Angle Measurement

6.1.4.2.

Coordinate Relationships

6.1.4.3.

6.2.

Trigonometric Identities

6.2.1.

Pythagorean Identities

6.2.2.

Angle Sum and Difference Formulas

6.2.3.

Double Angle Formulas

6.2.4.

Half Angle Formulas

6.3.

Inverse Trigonometric Functions

6.3.1.

Arcsine Function

6.3.1.1.

Definition and Range

6.3.2.

Arccosine Function

6.3.2.1.

Definition and Range

6.3.3.

Arctangent Functions

6.3.3.1.

Single-Argument Arctangent

6.3.3.2.

Two-Argument Arctangent

6.3.3.3.

Quadrant Determination

6.3.3.4.

Handling Edge Cases

6.4.

Trigonometry Applications

6.4.1.

Angle Calculations

6.4.1.1.

Angle Between Vectors

6.4.1.2.

Direction Calculations

6.4.1.3.

Orientation Determination

6.4.2.

Targeting Systems

6.4.2.1.

Calculating Firing Angles

6.4.2.2.

Trajectory Calculations

6.4.2.3.

Predictive Aiming

6.4.2.4.

Lead Calculations

6.4.3.

Motion Patterns

6.4.3.1.

Circular Motion

6.4.3.2.

Oscillatory Motion

6.4.3.3.

6.4.3.4.

Parametric Curves

6.4.4.

6.4.4.1.

Heading Calculations

6.4.4.2.

Turn Angle Determination

6.4.4.3.

Compass Bearings

6.4.4.4.

Pathfinding Applications

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