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Polar Coordinates. Lesson 10.5. •. 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.

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## Polar Coordinates

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**Polar Coordinates**Lesson 10.5**•**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)**Plot Given Polar Coordinates**• Locate the following**Find Polar Coordinates**• What are the coordinates for the given points? • A • A = • B = • C = • D = • B • D • C**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**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**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**Graphing Polar Equations**• Set Mode on TI calculator • Mode, then Graph => Polar • Note difference of Y= screen**Graphing Polar Equations**• Also best to keepangles in radians • Enter function in Y= screen**Graphing Polar Equations**• Set Zoom to Standard, • then Square**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**Assignment**• Lesson 10.5A • Page 433 • Exercises 1 – 45 odd • Lesson 10.5B • Page 433 • Exercises 47 – 61 odd

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