A couple days ago when I was working on the spiral experiment, I needed to read up a little bit on trigonometry because I realized that to calculate the x’s and y’s that I needed to plot, I needed to visualize a right triangle with point A at origin, B at my x coordinate, and C at my y coordinate. Given angle and a hypotenuse length, I could calculate my adjacent and opposite angles using the cosine and sine functions, respectively. Then, increase the hypotenuse length at the same rate as lines are drawn, et voila, you get a spiral.
But I wanted to understand sine better. I saw an animated diagram at the Wikipedia article that showed me how the sine function produced the typical sine wave graph, and how it related to the circle. But I still wanted more. I wanted to be the line and find out how given one number, the other number could be circumscribed either on the circumference of a circle, or transposed(?) onto the positive-x quadrants of a graph. Hence my experiment today.
Questions still lingering
- As I increased angle, my red line was moving clockwise on the circle. I thought increasing angle would move in a counter-clockwise direction. Is this just a move on the part of programming engines to try to be more logical than traditional math?
- As angle approached 90°, the y-coordinate decreased – why? I thought it should increase as angle approaches 90, then fall as it approaches 180, repeat.