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Created with Fabric.js 1.4.5 Polar and Rectangular Coordinates The rectangular coordinates (x,y) of a point named by the polar coordinates (r, θ) can be found by using the following formulas. x = r cos θ y = r sin θ Converting Polar to Rectangular Converting Rectangular to Polar The polar coordinates (r, θ)of a point named by the rectangularcoordinates (x,y) can be found by thefollowing formulas. r = x²+y² θ = Arctan y/x, when x>0 θ = Arctan y/x + pi, when x<0 Polar Coordinates: a grid of concentric circles and their center, which is called the pole , whose radii are integral multiples of 1. Rectangular Coordinates a pair of coordinatesmeasured along the axesat right angles to oneanother. Examples: Converting Polar to Rectangular: Converting Rectangular to Polar: a) P(5, pi/3)For P(5, pi/3), r = 5 and θ = pi/3.x = r cos θ y = r sin θ = 5 cos pi/3 = 5 sin pi/3 = 5(.5) or 5/2 = 53/3The rectangular coordinates of P are(5/2, 53/2). b) Q(-13, -70°)For Q(-13, -70°), r = -13 and θ = -70°x = r cos θ y = sin θ = -13 cos (-70°) = -13 sin (-70°) = -4.45 = 12.22The rectangular coordinates of Q are approximately (-4.45, 12.22) Find the polar coordinates of R(-8,-12)For R(-8,-12), x = -8 & y = -12r = x²+y² θ = Arctan y/x + pi = (-8)²+(-12)² = Arctan -12/-8 + pi = 208 = Arctan 3/2 + pi = 14.42 = 4.12The polar coordinates of R are approximately(14.42,4.12) Write the polar equation r = 6 cos θ in rectangular form.r = 6 cos θr² = 6rcos θ x² + y² = 6x
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