How can I convert polar coordinates to rectangular coordinates?
suppose you have a point (r,Ø)
Join the point to the origin and complete the right-angled triangle.
Call the point (r,Ø) as (x,y) in the rectangular system.
then
r^2 = x^2 + y^2
and tanØ = y/x
also :
x/r = cosØ ---> x = rcosØ
y/r=sinØ ---> y = rsinØ
Depending on the equation, you sometimes have to be very creative in converting from one system to the other.
Do you have an example?
To convert polar coordinates to rectangular coordinates, you can use the following formulas:
x = r * cos(theta)
y = r * sin(theta)
Here's how you can do it step by step:
1. Start with the given polar coordinates, (r, theta), where r represents the distance from the origin (pole) to the point, and theta represents the angle that the line segment connecting the origin to the point makes with the positive x-axis.
2. Use the formula x = r * cos(theta) to find the x-coordinate of the point. Multiply the distance r by the cosine of the angle theta, which gives you the x-coordinate.
3. Use the formula y = r * sin(theta) to find the y-coordinate of the point. Multiply the distance r by the sine of the angle theta, which gives you the y-coordinate.
4. The rectangular coordinates of the point are (x, y), representing the x-coordinate and y-coordinate respectively.
For example, let's say you have polar coordinates (r, theta) = (3, 45 degrees). Applying the formulas:
x = 3 * cos(45 degrees)
= 3 * (√2 / 2)
= √2 * 3 / 2
= 3√2 / 2
y = 3 * sin(45 degrees)
= 3 * (√2 / 2)
= √2 * 3 / 2
= 3√2 / 2
So, the rectangular coordinates are approximately (x, y) = (3√2 / 2, 3√2 / 2).