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SELFMADE
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I am going to have a test on polar coordinates next week. What are the most important things to remember?
Cartesian coordinates use x and y coordinates to specify a point on a plane, while polar coordinates use a distance from the origin and an angle to specify a point.
To convert from Cartesian coordinates (x, y) to polar coordinates (r, θ), use the equations r = √(x² + y²) and θ = tan⁻¹(y/x). To convert from polar coordinates to Cartesian coordinates, use the equations x = r cos(θ) and y = r sin(θ).
The important points in polar coordinates are the origin (0,0), the pole (r,0), and points on the positive and negative x-axis (r, π/2 and r, 3π/2 respectively).
To plot a point in polar coordinates, first find the distance from the origin (r) and the angle from the positive x-axis (θ). Then, starting from the pole, use a compass to measure the distance r and a protractor to measure the angle θ, and mark the point on the polar plane.
Polar coordinates are often used in engineering, physics, and navigation. They are commonly used to describe the location of objects in circular motion, such as planets orbiting around the sun. They are also used in GPS systems to determine the location of an object on the Earth's surface.