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Intro to Polar Coordinates

Intro to Polar Coordinates. •. θ. r. Points on a Plane. Rectangular coordinate system Represent a point by two distances from the origin Horizontal dist, Vertical dist Also possible to represent different ways Consider using dist from origin, angle formed with positive x-axis. (x, y). •.

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Intro to Polar Coordinates

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  1. Intro to Polar Coordinates

  2. • θ r Points on a Plane • Rectangular coordinate system • Represent a point by two distances from the origin • Horizontal dist, Vertical dist • Also possible to represent different ways • Consider using dist from origin, angle formed with positive x-axis (x, y) • (r, θ)

  3. Plot Given Polar Coordinates • Locate the following

  4. Find Polar Coordinates • What are the coordinates for the given points? • A • A = • B = • C = • D = • B • D • C

  5. Converting Polar to Rectangular • Given polar coordinates (r, θ) • Change to rectangular • By trigonometry • x = r cos θy = r sin θ • Try = ( ___, ___ ) • r y θ x

  6. Converting Rectangular to Polar • • Given a point (x, y) • Convert to (r, θ) • By Pythagorean theorem r2 = x2 + y2 • By trigonometry • Try this one … for (2, 1) • r = ______ • θ = ______ r y θ x

  7. Polar Equations • States a relationship between all the points (r, θ) that satisfy the equation • Example r = 4 sin θ • Resulting values Note: for (r, θ) It is θ (the 2nd element that is the independent variable θ in degrees

  8. Graphing Polar Equations • Set Mode on TI calculator • Mode, then Graph => Polar • Note difference of Y= screen

  9. Graphing Polar Equations • Also best to keepangles in radians • Enter function in Y= screen

  10. Graphing Polar Equations • Set Zoom to Standard, • then Square

  11. Try These! • For r = A cos Bθ • Try to determine what affect A and B have • r = 3 sin 2θ • r = 4 cos 3θ • r = 2 + 5 sin 4θ Experiment with Polar Function Spreadsheet

  12. Write Polar Equation in Rectangular Form • Given r = 2 sin θ • Write as rectangular equation • Use definitions • And identitiesGraph the given equation for clues

  13. Write Polar Equation in Rectangular Form • Given r = 2 sin θ • We know • Thus • And

  14. Write Rectangular Equation in Polar Form • Consider 2x – 3y = 6 • As before, usedefinitions

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