Module 27  Polar Functions 
Introduction  Lesson 1  Lesson 2  Lesson 3  SelfTest 
Lesson 27.1: Polar Coordinates 
Polar coordinates are an alternative way of identifying points in a plane. They are useful in many applications. For certain types of regions and curves, working in polar coordinates is much easier than working with (x, y) coordinates. Polar coordinates will be explored in this lesson and you will learn how to convert points given in rectangular coordinates to polar coordinates and viceversa. Defining Polar Coordinates When assigning rectangular coordinates (x, y) to a point P in the plane, x is the horizontal distance and y is the vertical distance from the origin O to the point P. If polar coordinates (r, ) are used instead, r is the directed distance from the origin to the point P and is the directed angle from the positive xaxis to ray OP. Recall that there are an infinite number of angles that are coterminal with . Because any one of these angles can be used, there are infinitely many possible polar coordinates for each point in the plane. Converting Rectangular Coordinates to Polar Coordinates The TI83 has features that convert coordinates from rectangular to polar and viceversa. Suppose you wish to find a value of r for the rectangular point (3, 2).
This item returns the value of the r polar coordinate for a point given in rectangular coordinates.
The distance from the origin O to the point (3, 2) is about 3.6056, so the polar coordinate r is about 3.6056. A value of for this point may be found using a similar procedure.
The rectangular point (3, 2) is represented as approximately (3.61, 0.588) in polar coordinates. Because the calculator is in Radian mode, the angle measurement is given in radians. 27.1.1 If (r, ) are polar coordinates for a point P, what are the other possible polar coordinates for P? Click here for the answer. Converting from Polar to Rectangular Coordinates 27.1.2 Use the and features in the Angle menu to find the x and ycoordinates for the polar point . Click here for the answer. Unlike polar coordinates, the rectangular coordinates for any given point in the plane are unique. 
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