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