rectangular to polar coordinates?

Imagine a segment drawn from the origin to the point (x,y). You can use this to get the equations for transforming to polar coordinates. Note that the length of the segment is r. If you form a right triangle, then x=r cos Θ and y = r sin Θ.

This gives (r cos Θ)(r sin Θ) = 1

r^2 sin Θ cos Θ = 1

Now we can use the identity sin 2Θ = 2 sin Θ cos Θ.

sin Θ cos Θ = 1/2 sin 2 Θ

Substituting gives,

r^2 1/2 sin 2 Θ = 1 or

r^2 sin 2Θ = 2

First, draw out the oblong coordinates, and you will possibly have 2 sides to a triangle. The third area is going from the muse to the factor that the oblong coordinates specifiy. Then, in simple terms use trigonometry (SOHCAHTOA) to locate the perspective and the dimensions of the hypotenuse. those 2 issues are used to grant the "polar coordinates" of that comparable factor. In different words, that's in simple terms a distinctive thank you to get to an identical factor. one way--oblong coordinates--you're instructed how far to circulate left and how far up. (or top and down, yet you get the belief). any incorrect way--polar coordinates--you tell what proportion stages to rotate, then how far to circulate in that course.