Intro to Polar Coordinates Objectives: Be able to graph and convert between rectangular and polar coordinates. Be able to convert between rectangular and.

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Presentation transcript:

Intro to Polar Coordinates Objectives: Be able to graph and convert between rectangular and polar coordinates. Be able to convert between rectangular and polar equations. TS: Examine Information from more than one point of view. Warm Up: If I were to turn 3π/4 degrees from the positive x-axis and then walk out 4 units from the origin in that direction, find the coordinates of the point I would be standing on.

Polar Coordinate System A point in the Polar coordinate system is (r, θ), where r is the directed distance from the pole and θ is the directed angle from the polar axis

Graphing Polar Coordinates A (1, π/4) B (3, - π/3) C (3, 5π/3) D (-2, -7π/6) E (-1, 5π/4)

Conversions between rectangular and polar Given (r, θ), the point (x, y) would be in the same location given all the following relations were true. x = rcosθ r 2 = x 2 + y 2 y = rsinθ

Graphing Polar Coordinates (-√2, 3π/4) Convert to Rectangle, Graph both.

Use the conversions to change the given coordinates to their Polar Form (-4, -4) (-1, √3)

Converting/Graphing Equations Polar to Rectangular 1)r = 2

Converting/Graphing Equations Polar to Rectangular 2)θ = π/3

Converting/Graphing Equations Polar to Rectangular 3) r = secθ

Converting/Graphing Equations Rectangular to Polar 4) x 2 + y 2 = 16

Converting/Graphing Equations Rectangular to Polar 5) y = x

Converting/Graphing Equations Rectangular to Polar – Convert to polar form. Identify the figure and graph it. Confirm by graphing the polar as well on your calculator 6) x 2 + y 2 – 8y = 0

More Challenging Conversions 7) Polar to Rectangular

More Challenging Conversions 8) Rectangular to Polar (x – 1) 2 + (y + 4) 2 = 17

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