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Polar Coordinates
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Intro to Polar CoordinatesLesson 6.5A
*Points on a PlaneRectangular coordinate systemRepresent a point by two distances from the originHorizontal dist, Vertical dist
Also possible to represent different waysConsider using dist from origin, angle formed with positive x-axis(x, y)(r, )
*Plot Given Polar CoordinatesLocate the following
*Find Polar CoordinatesWhat are the coordinates for the given points? B A C D A =
B =
C =
D =
*Converting Polar to RectangularGiven polar coordinates (r, )Change to rectangular
By trigonometryx = r cos y = r sin
Try = ( ___, ___ )rxy
*Converting Rectangular to PolarGiven a point (x, y)Convert to (r, )
By Pythagorean theorem r2 = x2 + y2
By trigonometry
Try this one for (2, 1) r = ______ = ______rxy
*Polar EquationsStates a relationship between all the points (r, ) that satisfy the equationExampler = 4 sin Resulting values in degreesNote: for (r, ) It is (the 2nd element that is the independent variable
*Graphing Polar EquationsSet Mode on TI calculatorMode, then Graph => Polar
Note difference of Y= screen
*Graphing Polar EquationsAlso best to keep angles in radians
Enter function in Y= screen
*Graphing Polar EquationsSet Zoom to Standard,
then Square
*Try These!For r = A cos B Try to determine what affect A and B have
r = 3 sin 2r = 4 cos 3r = 2 + 5 sin 4Experiment with Polar Function Spreadsheet
*Assignment ALesson 6.5APage 424Exercises 1 47 odd
Polar CoordinatesLesson 6.5B
*Write Polar Equation in Rectangular FormGiven r = 2 sin Write as rectangular equationUse definitionsAnd identities (see inside back cover)Graph the given equation for clues
*Write Polar Equation in Rectangular FormGiven r = 2 sin
We know
Thus
And
*Write Rectangular Equation in Polar FormConsider 2x 3y = 6
As before, use definitions
*Assignment BLesson 6.5BPage 424Exercises 49 73 odd