6.4 - Polar Coordinates HW: Pg. 539 #16-26

Polar Coordinate System A polar coordinate system is a plane with a point O, the pole, and a ray from O, the polar axis. Each point P in the plane is assigned polar coordinates: r is the directed distance from O to P, and  is the directed angle whose initial side is on the polar axis and whose terminal side is on the line OP. P(r,) Pole O  Polar axis

X-Y vs. Polar X-Y COORDINATE POLAR COORDINATE

Plot the points with the given polar coordinates Q(-1,3π/4) R(3,-45)

Plot the points with the given polar coordinates B(-2,-π) C(-3,3π/2) D(4,7π/2) E(5,-120) F(-7,300 )

Finding all polar coordinates for a point If the point P has polar coordinates (3,π/3), find all polar coordinates for P. Polar Graphs

Finding all Polar Coordinates of a Point Let P have polar coordinates (r,). Any other polar coordinate of P must be of the form (r, + 2nπ) or (-r,+(2n + 1)π) Where n is any integer. In particular, the pole has polar coordinates (0,), where  is any angle.

Polar coordinates of point P are give Polar coordinates of point P are give. Find all of its polar coordinates. P = (2,π/6) P = (1.5, -20)

Coordinate Conversion Let the point P have polar coordinates (r,) and rectangular coordinates (x,y). Then x = rcos , r2 = x2 + y2, y = rsin , tan  = y/x

Find the rectangular coordinates of the points with the given polar coordinates Q(2,-200)

Find two polar coordinate pairs for the points with given rectangular coordinates Q(-3,0)

Using a Grapher to Convert Coordinates Use our grapher to check the conversions Use your grapher to convert the polar coordinate pairs (2,π/3), (-1,π/2), (2,π), (-5,3π/2), (3,2π), to rectangular coordinate pairs. Use your grapher to convert the rectangular coordinate pairs (-1,-3), (0,2), (3,0), (-1,0), (0,-4) to polar coordinate pairs.

Convert r = 4sec  to rectangular form and identify the graph Convert r = 4sec  to rectangular form and identify the graph. Support your answer with a polar graphing utility.

HW: Pg. 540 #36-40e,