Today in Precalculus Go over homework Need a calculator Notes: Converting between Polar and Rectangular Equations Homework

Graphing Polar Equations Change calculator mode to POL and radians Type in r = 5cos(2 θ) (use X,T,θ,N button for θ) Zoom - standard Graph

Converting Equations - HINTS To convert from polar to rectangular: a.If equation has sinθ or cosθ, multiply both sides by r. Then convert to x and/or y (x=rcosθ and y=rsinθ ) b.Convert r 2 to x 2 + y 2 c.Rewrite secθ as and cscθ to d.Complete the square if necessary. e.(x – a) 2 + (y – b) 2 = r 2 Equation of a circle with center (a,b) and radius r.

Example 1 Convert to rectangular, identify the type of equation and check the graph. r = – 4secθ r = – 4 rcosθ = – 4 x = -4 A vertical line

Example 2 Convert to rectangular, identify the equation, and check graph. r = 2cosθ + 2sinθ r 2 = 2rcosθ + 2rsinθ (multiply both sides by r) x 2 + y 2 = 2x + 2y x 2 – 2x + y 2 – 2y = 0 x 2 – 2x y 2 – 2y + 1 = (complete the square) (x – 1) 2 + (y – 1) 2 = 2 Circle with center (1,1) and radius of

Converting Equations - HINTS To convert from rectangular to polar: a.Multiply out any squared binomial terms like (x – 3) 2 b.Replace x with rcosθ and y with rsinθ c.Replace x 2 + y 2 with r 2 d.solve for r (may need to factor)

Example 1 2x – y = 5 (equation of a line, y-int. -5, slope 2) 2rcosθ – rsinθ = 5 r(2cosθ – sinθ ) = 5

Example 2 (x – 2) 2 + y 2 = 4(circle: center (2,0) radius 2) x 2 – 4x y 2 = 4 (multiply squared binomials) x 2 + y 2 – 4x = 0 r 2 – 4rcosθ = 0 (replace x 2 + y 2 with r 2 and x with rcosθ) r(r – 4cosθ ) = 0(factor r) r = 0 r – 4cosθ = 0(set terms equal to zero) r = 4cosθ(solve for r) r = 0 is a point at the pole r=4cosθ is the equation

Homework Pg. 540: 35-49odd