4. Sinewaves

Brackeys video: Sinewaves

Sine and cosine

• Script reference: Mathf.Sin
• and are oscillating functions that return a value between and
  • here, is an angle measured in radians (rad).
• Their form is the same, but is shifted from by rad:
  
  

Degrees vs. radians

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Sin & Cos triangle definition

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Circular motion

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Extra: Polar coordinates

• Wikipedia: Polar coordinate system
• Any two-dimensional vector can be represented by its length and rotation angle
  
  

Code example

double phi = Mathf.pi/2;
double r = 5.0f;

Vector2 vec = new Vector2(
    r * Mathf.Cos(phi),
    r * Mathf.Sin(phi)
);

From cartesian ( and ) to polar coordinates ( and )

• What about the other way around?
  
  
  • is an important function in game development
  • Script Reference: Mathf.Atan2
• In code:

  Vector2 vec = new Vector2(4.0f, 2,0f);
  
  double r = vec.Magnitude;
  double phi = Mathf.Atan2(vec.y, vec.x);