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Chapter 9: Q. 85 (page 568)

In converting from polar coordinates to rectangular coordinates, what formulas will you use?

Short Answer

Expert verified

To convert polar coordinates (r,θ)to rectangular coordinates (x,y)we use the formulas

x=rcosθy=rsinθ

Step by step solution

01

Step 1. Given

In a rectangular coordinate system a point in the plane is represented by an ordered pair of numbers (x,y), where x and y equal the signed distance of the point from the y-axis and x-axis, respectively.

A point in a polar coordinate system is represented by an ordered pair of numbers (r,θ). If r>0, then r is the distance of the point from the pole; θ is an angle formed by the polar axis and a ray from the pole through the point.

02

Step 2. Formula Used

If P is a point with polar coordinates (r,θ), the rectangular coordinates (x,y) of P are given by

x=rcosθy=rsinθ

Using these formulas we can convert a given polar coordinate into its equivalent rectangular coordinate.

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Most popular questions from this chapter

Identify and graph each polar equation. Verify your graph using a graphing utility.

r=1-cosθ

find the unit vector in the same direction asv

v=-5i+12j

Use the vectors in the figure at the right to graph each of the following vectors.

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Identify and graph each polar equation. Verify your graph using a graphing utility.
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Identify and graph each polar equation. Verify your graph using a graphing utility.

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