Looking at things from a fresh Angle.

• Radians vs Degrees
  • We are all comfortable that a circle can be divided into $360^\circ$
  • But we also know that the c++ trig functions want radians.
  • What is a radian?
    • wikipedia reference
    • This is the SI unit for measuring an angle.
    • It is a dimensionless unit,
    • An angle is measured between 0 and $2\pi$ radians.
  • Converting:
    • $2\pi $ radians = $360^\circ$
    • or $\frac{2\pi}{360}$
    • which simplifies to $\frac{\pi}{180}$
  • We need this because all trig functions take radians.
• But I don't know trig functions.
  • Ok, but well....
  • The functions cos and sin are used to compute the relationship between various angels of a right triangle.
    • Given a right triangle (or a triangle with a $90^\circ$ angle.
    • (Wikipedia)
  • (Wikipedia)
  • $\cos(\theta) = \frac{adjacent}{hypotenuse}$
  • $\sin(\theta) = \frac{opposite}{hypotenuse}$
  • $\tan(\theta) = \frac{adjacent}{opposite}$
  • sin and cos are great functions
  • (Wikipedia again)
• These are the basis for Polar Coordinates
  • The is an alternative way to describe a plane.
  • Alternative to Cartesian.
  • r is a distance from the origin
  • $\Theta$ is an angle from the "x" axis.
  • $x = r\cos(\Theta))$
  • $y = r\sin(\Theta))$
  • But first ctx.arc
    • reference
    • arguments
      • center x
      • center y
      • radius
      • Start angle
      • end angle
      • counterclockwise
        • optional bool direction to draw,
        • default is false
    • Use ctx.beginPath and ctx.stroke or ctx.fill
  • A demo
• But I don't want to use those...
  • Ok, derive everything from $r^2 = (x - x_c)^2 + (y - y_c)^2$
    • where $(x_c, y_c)$ is the center of the circle.
    • and $r$ is the radius of the circle