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MAT187H1 F LEC0101 Polar Coordinates (Pre-Class Essentials)

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Match each polar equation to its graph For the more complicated formulas, you can test your choice by plugging in specific values for r and θ. r=2  [ Select ] A B D C θ= π 4  C r= 2 sinθ [ Select ] B C A D r=cos(2θ)  [ Select ] C B D A  

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The task presents four polar equations and four graph labels (A, B, C, D) and asks you to match each equation to its graph. We will examine the key features of each equation so you can reason about which graph label best fits each one. Since the actual graph images for A, B, C, and D aren’t provided here, I’ll describe the typical shape each equation produces and then discuss how to reason about the likely match with each graph label. 1) r = 2 - What it describes: In polar coordinates, r = 2 is a circle of radius 2 centered at the origin. Every angle θ yields the same radius 2 point, so the locus is the circle x^2 + y^2 = 4 in Cartesian terms. - How this helps with matching: Look for a circle centered at the origin with radius 2. Any graph labeled with this circle should be the correct m......Login to view full explanation

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