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Warm-up:

Warm-up:. Math ador Gameplan. Section 9.3: P olar and Rectangular Coordinates CA Standards: T15.0 Daily Objective (2/28/13): Students will be able to convert between polar and rectangular coordinates. Homework: page 572 (#14 to 39 all ).

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Warm-up:

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  1. Warm-up:

  2. MathadorGameplan Section 9.3:Polar and Rectangular Coordinates CA Standards: T15.0 Daily Objective (2/28/13): Students will be able to convert between polar and rectangular coordinates. Homework:page 572 (#14 to 39 all)

  3. Convert: Polar Coordinates  Rectangular Coordinates

  4. Find the rectangular coordinates for the point y = -1.7 x = -1 Rectangular coordinates: (-1, -1.7)

  5. Convert: Polar Coordinates  Rectangular Coordinates • (-4.5, 7.8) • (-4.2, -4.2) • (0, -3) • (9, 2π/3) • (6, 5π/4) • (-3, π/2)

  6. Convert: Rectangular Coordinates  Polar Coordinates OR

  7. Find the polar coordinates for the point such that r > 0 and 0 ≤ θ< 2π Polar Coordinates

  8. Convert: Rectangular Coordinates  Polar Coordinates • (2.8, 3π/4) • (7, 0) • (5, 3π/2) • (-2, 2) • (7, 0) • (0, -5)

  9. Converting equations from 1 system to another • We can use the conversion equations to convert from one coordinate system to another.

  10. Convert the rectangular equation to a polar equation. Express r in terms of Ѳ.

  11. Convert: rectangular eqn.  polar eqn.(x -1)2 + y2= 1 (x -1)2 + y2= 1 x2 – 2x + 1 + y2 = 1 x2 + y2 – 2x = 0 r2 – 2rcos θ = 0 r2 = 2rcos θ r = 2cos θ

  12. PRACTICEConvert each rectangular equation to a polar equation that expresses r in terms of θ.a) 3x - y = 6b) x2+ (y – 3)2 = 9

  13. Convert each polar equation to a rectangular equation in x and y: r = 5 r = 5 r2 = 25 x2 + y2 = 25

  14. Convert: Polar Eqn Rectangular Eqn

  15. Convert: Polar Eqn Rectangular Eqn r = -6 cos θ r2= -6r cos θ x2 + y2= -6x Let’s complete the square x2 + 6x + y2= 0 x2 + 6x+9 + y2= 9 (x + 3)2+ y2= 9 This is a circle centered at (-3, 0) radius 3

  16. Convert each polar equation to a rectangular equation in x and y: r = 8 csc θ r = 8 csc θ r sin θ = 8 y = 8

  17. PRACTICE Convert each polar equation into a rectangular equation in x and y. • r = 4 • θ = 3π/4 • r = -2 sec θ • r = 10 sin θ

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