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Goals : Graph polar equations and determine the symmetry of polar graphs.

AP Calculus BC – Chapter 10 Parametric, Vector, and Polar Functions 10.5: Polar Coordinates and Polar Graphs. Goals : Graph polar equations and determine the symmetry of polar graphs. Convert Cartesian equations into polar form and vice versa. Polar Coordinates:.

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Goals : Graph polar equations and determine the symmetry of polar graphs.

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  1. AP Calculus BC – Chapter 10Parametric, Vector, and Polar Functions 10.5: Polar Coordinates and Polar Graphs Goals: Graph polar equations and determine the symmetry of polar graphs. Convert Cartesian equations into polar form and vice versa.

  2. Polar Coordinates: In polar coordinates, we identify the origin O as the pole and the positive x-axis as the initial ray of angles measured in the usual trigonometric way. We can then identify each point P in the plane by polar coordinates (r, ), where r gives the directed distance from O to P and  gives the directed angle from the initial ray to the ray OP.

  3. Polar Coordinates: Example 1: (a) Find rectangular coordinates for the points with given polar coordinates. (i) (4, π/2) (ii) (-3, π) (iii) (16, 5 π /6) (iv) (-√2, - π /4) (b) Find two different sets of polar coordinates for the points with given rectangular coordinates. (i) (1, 0) (ii) (-3, 3) (iii) (0, -4) (iv) (1, √3)

  4. Polar Coordinates: Example 2: Graph all points in the plane that satisfy the given polar equation. (a) r=2 (b) r=-2 (c)  = π/6

  5. Polar Coordinates: Example 3: Find an appropriate graphing window and produce a graph of the polar curve. (a) r=sin (b) r=1-2cos (c) r=4sin

  6. Equations: Polar-Rectangular Conversion Formulas: x=r cos r2 = x2 + y2 y= r sin tan = y/x Parametric Equations of Polar Curves: The polar graph of r=f() is the curve defined parametrically by: x=r cos = f()cos y=r sin = f()sin

  7. Assignment and Notes: • HW 10.5: #1, 3, 5, 9, 15, 21, 27, 39, 43, 54, 55, 57, 67. Test Friday, March 16. Sign up and pay for your AP Calculus BC exam by today.

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