Direction Of Velocity Using Sine & Cosine

In this demo, the velocity of the object is specified by variables for direction and speed rather than x and y components. The direction is a value for t, as described in the definition of sine and cosine. When it comes time to move the object, x and y velocity components are found by cos(t) and sin(t), respectively. Programming it this way makes it easier to "steer" the object.

Since a point (cos(t), sin(t)) is a distance of 1 from the origin, moving x by cos(t) and y by sin(t) will move the object a distance of 1. If the components are multiplied by speed, the object will move a distance of speed.

How is the car steered in terms of the variables in the program?

Why is yVelo set to negative sine? The unit circle is drawn on a standard coordinate system, with y getting larger upward. The y coordinates get flipped upside-down on the Director stage since locv gets larger downward. Taking negative sine compensates for this.

Similarly, why is sprite rotation set to negative tCar? A sprite turns clockwise as its rotation property increases, while in the definition of sine and cosine, t increases in a counter-clockwise direction.

Another way to compensate for both these is to write the math as if t gets larger going clockwise around the unit circle, rather than counter-clockwise. So that steering left means subtracting from t, and steering right means adding.

Because the direction t=0 points to the right, the car cast member was created pointing to the right. This makes it possible to use t to set the sprite rotation without having to shift it. For example, if the car was created pointing upward, 90 degrees (or pi/2 radians) would have to be added when setting the sprite rotation property. Otherwise the car would appear to travel sideways.

•Why don't xVelo, yVelo, or speed need to be declared as properties or initialized in this program? How would you make the car accelerate smoothly, instead of starting and stopping suddenly?