Lesson 2

1. Lesson 2 By us

2. Movement • moving left/right/up/down is easy • so are rotations • but if the goal is to move diagonally, there is a problem • the solution is trigonometry

3. The Right Triangle • every triangle has 3 sides • the sum of internal angles is 180 degrees • a2 + b2 = c2 c b a

4. Trig • let ‘x’ be an angle • sin(x) = opposite / hypotenuse • cos(x) = adjacent / hypotenuse • tan(x) = opposite / adjacent • you will never use “tan” in programming • “sin” and “cos” are crucial

5. Trig 2 • sin(z) = opposite / hypotenuse • cos(z) = adjacent / hypotenuse • tan(z) = opposite / adjacent

6. Trig 3 the scenario: • you have the angle (this._rotation) • you have the hypotenuse (speed) • now you need vertical length and horizontal length

7. Trig 4 Math.sin (z) = y / velocity  y = Math.sin (z) * velocity Math.cos (z) = x / velocity  x = Math.cos (z) * velocity

8. Trig 5 • so now that you have ‘x’ (horizontal displacement) • you also have ‘y’ (vertical displacement) ie: this._x += Math.cos (z) * velocity; this._y -= Math.sin (z) * velocity;

9. WAIT A MINUTE • the input for Math.sin () or Math.cos () is in radians • 1 radian = PI / 180 degrees • 1 degree = 180 / PI radians • to get PI, you type: Math.PI

10. More Radians example: z = z*Math.PI/180; //or z *= Math.PI/180; this._x += Math.cos (z) * velocity; this._y -= Math.sin (z) * velocity;

11. DONE FOR TODAY!