Polar Coordinates (MAT 170) Sections 6.3

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Presentation transcript:

Polar Coordinates (MAT 170) Sections 6.3

Objectives Plot point in the polar coordinate system Find multiple sets of polar coordinates for a given point Convert between polar and rectangular coordinates Convert between equations given in rectangular coordinates and equations given in polar coordinates

Plot the point

Multiple Representations of Polar Points Polar Coordinates (MAT 170) Multiple Representations of Polar Points if n is any integer, the point (r, θ) can be represented as

Find another representation (in polar coordinates) for the point Polar Coordinates (MAT 170) Find another representation (in polar coordinates) for the point

Relationships Between Polar and Rectangular Coordinates Polar Coordinates (MAT 170) Relationships Between Polar and Rectangular Coordinates

Find the rectangular coordinates for the point Polar Coordinates (MAT 170) Find the rectangular coordinates for the point

Polar Coordinates (MAT 170) Find the polar coordinates for the point (given in rectangular coordinates) such that r > 0 and 0 ≤ θ < 2π

Polar Coordinates (MAT 170) Convert the rectangular equation to a polar equation. Express r in terms of θ.

Convert the polar equation to a rectangular equation. Polar Coordinates (MAT 170) Convert the polar equation to a rectangular equation.

Convert the polar equation to a rectangular equation. Polar Coordinates (MAT 170) Convert the polar equation to a rectangular equation.