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Chapter 9: Q. 79 (page 568)

The letters r and 胃represent polar coordinates. Write each equation using rectangular coordinates (x,y).

r=2

Short Answer

Expert verified

The equation is written using rectangular coordinates asx2+y2=4.

Step by step solution

01

Step 1. Given Information

We are given an equation r=2.

We need to write the equation using rectangular coordinates.

02

Step 2. Convert into rectangular coordinates   

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

x=rcos胃y=rsin胃

And it implies that

x2+y2=r2

03

Step 3. Convert into rectangular coordinates 

In the given equation r=2, we square both sides

r=2r2=22r2=4

Now using the relation r2=x2+y2the equation can be written as

r2=4x2+y2=4

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Most popular questions from this chapter

Findzwand zw. Leave the answers in polar form.

role="math" localid="1646661399572" z=2+2iw=3-i

Write the expression in the standard form a+bi.

3cos10掳+isin80掳3

In Problems 13鈥�28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

rsin胃=4

Match the graph with the polar equation.

r=2sin胃

Match the graph with the polar equation

rsin胃=2
See all solutions

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