Polar Coordinates and Graphing Section 10.5a

Polar Coordinates To define polar coordinates, we first fix an origin O (called the pole) and an initial ray from O. Then each point P can be located by assigning to it a polar coordinate pair : Directed distance from O to P Directed angle from initial ray to ray OP Origin (Pole) O Initial ray

Polar Coordinates Important note: The polar coordinates for any given point are not unique!!! Example: Plot the given point, and find two other sets of polar coordinates that define the point. Origin (Pole) O Initial ray

Guided Practice Plot the points with the given polar coordinates and find their Cartesian coordinates. Cartesian coordinates: y x

Guided Practice Plot the points with the given polar coordinates and find their Cartesian coordinates. Cartesian coordinates: y x

Guided Practice Plot the points with the given Cartesian coordinates and find two sets of polar coordinates for each. Polar coordinates: y x

Guided Practice Plot the points with the given Cartesian coordinates and find two sets of polar coordinates for each. y Polar coordinates: x

Polar Graphing Equation Polar Graph Circle of radius centered at Line through making an angle with the initial ray Examples: and are equations for the circle of radius 1 centered at : O x

Polar Graphing Equation Polar Graph Circle of radius centered at Line through making an angle with the initial ray Examples: , , and are equations for the line: O x

Guided Practice Graph the set of points whose polar coordinates satisfy the given conditions. y x

Guided Practice Graph the set of points whose polar coordinates satisfy the given conditions. and y x

Guided Practice Graph the set of points whose polar coordinates satisfy the given conditions. and y x

Guided Practice Graph the set of points whose polar coordinates satisfy the given conditions. and y x

Guided Practice Graph the set of points whose polar coordinates satisfy the given conditions. y x