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# WKS4 - Worksheet 4 Math 126 The goal of this worksheet is...

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Worksheet 4 Math 126 The goal of this worksheet is to get familiar with the use of polar coordinates and to practice the conversion from polar coordinates to Cartesian and vice versa. You should observe that some regions are easier to understand in Cartesian coordinates whereas for others the choice of polar coordinates is much more suitable. The skill of being able to chose the right coordinate system will be invaluable when we start evaluating double integrals as in chapter 15. Later on you may wish to compare the regions you sketch today with the ones in problems 1-6, Section 15.4. The following trig identity will be useful for the worksheet: sin( α + β ) = sin( α ) cos( β ) + cos( α ) sin( β ) cos( α + β ) = cos( α ) cos( β ) - sin( α ) sin( β ) And here are the conversion formulas x = r cos θ, y = r sin θ r 2 = x 2 + y 2 , tan θ = y x 1. Describe each curve (region) below in Cartesian coordinates. Then sketch the curve (region). Indicate which coordinate system you used for sketching.

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WKS4 - Worksheet 4 Math 126 The goal of this worksheet is...

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