The first coordinate in rectangular coordinates (usually denoted x) measures the distance from a vertical axis and the second coordinate (usually denoted y) measures the distance from the horizontal axis. In polar coordinates the first coordinate (usually denoted r) measures the distance from the origin, and the second coordinate (usually denoted θ) measures the angle in standard position from the positive horizontal axis.
With this in mind, name the coordinates of the following marked point in both rectangular and polar form and mark the same point on the polar grid:
1.) Find two other names in polar coordinates for the following point which is also given in polar coordinates. Use a positive r value for one name and a negative r value for the other name.
Given point: (√(13), 56.31°)
2.) Let's graph the following polar equation: r = 5 sin(θ)
3.) Convert (-3, -4) to polar coordinates.
Let's derive the conversion formulas for polar to rectangular and vice-versa:
4.) Convert x2 + y2 - 4x + 3y = 0 to a polar equation.
5.) Convert the equation in number 2 to a rectangular equation.