How to Convert Trigonometry Polar Points to Rectangular Points
You can describe the coordinates of a point (P) either by the rectangular or polar coordinate systems. In the rectangular coordinate system, you denote the point P as P(x, y) but in the polar coordinate system this same point would be P(r, θ). For many trigonometry problems, you need to know coordinate system conversion formulas. Learn to convert polar points to rectangular points with this tutorial.
Other People Are Reading
Instructions
-
-
1
Understand that the polar coordinates of the point P are (r, θ), where r is the distance from the origin and θ is the angle. You relate (r, θ) to the same point (x,y) in the rectangular system by using conversion formulas (see Resources).
-
2
Know the polar-rectangular conversion formulas to solve these type problems. These are: r²=x² + y², tan θ=y/x, θ=arctan y/x, x=rcos θ and y=rsin θ.
-
-
3
Convert the polar point to (-2, 270°) to a rectangular point by using the formulas in Step 2. Use this as an example to find the equivalent (x, y) values.
-
4
Use the formulas x=rcos θ and y=rsin θ to perform the conversion.
-
5
Substitute r=-2 and θ=270° into the formulas in Step 4 to get x=-2cos(270°) and y=-2 sin(270°).
-
6
Find the value for cos (270°) and sin (270°) by using the calculator to get that cos (270°) = 0 and sin (270°) = -1.
-
7
Place the values from Step 6 into the equation in Step 5 and solve for x and y. You find that x=-2cos(270°)=-2x(0)=0 and y=-2 sin(270°)=-2x(-1)=2. The point (0, 2) is the equivalent rectangular point found for the polar point (-2, 270°). To convert from rectangular to polar points use the formulas in Step 2 but solve for r and θ instead.
-
1
