Polar Coordinates Today’s Objective: I can convert between polar coordinates/equations and rectangular coordinates/equations.

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Presentation transcript:

Polar Coordinates Today’s Objective: I can convert between polar coordinates/equations and rectangular coordinates/equations.

1. Determine the quadrants containing the terminal side of angle: −4π/3. 2. Find a positive and negative angle coterminal with the given angle: −π/3. 3. Write a standard form equation for the circle with center at (−6, 0) and a radius of 4. Find the measure of the third side of the given triangle. 4.

Polar Coordinate System The Pole: point O Polar Axis: ray from point O (along positive x-axis) Polar Coordinates: (r, θ) r: directed distance from O θ: directed angle from polar axis Plot the points with the given polar coordinates. P (2, π/3) Q (−1, 3π/4) R (3, −45°)

Finding All Points Let the P have the polar coordinates (r, θ). Any other polar coordinate of P must be: (r, θ + 2πn) where n is any integer. Find all polar coordinates of the point (−5, 35°). (r, θ + 2πn) (−5, 35°+360°n) (−r, θ + (2n + 1) π) (5, 35°+(2n+1)180°) (5, 215°+360°n) or (−r, θ + (2n + 1) π)

Coordinate Conversion Pole = originpolar axis = positive x-axis

Equation Conversion Convert polar equations to rectangular form and identify the graph. Verify both equations using the polar mode on your calculator.

Equation Conversion A single point which is on the circle

Finding Distance using Polar Coordinates Pg. 492 #3-54 by 3s Radar detects two airplanes at the same altitude. Their polar coordinates are (8 mi, 110°) and (5 mi, 15°). How far apart are they?