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Chapter 9: Q. 4 (page 774)

Fill in the blanks to convert between rectangular coordinates and polar coordinates.

θ=.......

Short Answer

Expert verified

The value ofθ=tan-1yx

Step by step solution

01

Step 1. Given information

Polar coordinate has an angle θ

02

Step 2. Convert angle into rectangular coordinate.

Draw a diagram of circle of radius rand let a point localid="1652262156969" P(x,y)on the circle

Let the rectangular point (x,y)

So in the polar plane, we can see that in the right-angle triangle,

tanθ=yxθ=tan-1yx

Suppose if rectangular coordinates of a point is (1,2)

Thenθ=tan-121

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Most popular questions from this chapter

Measurements indicate that Earth’s orbital eccentricity is 0.0167and its semimajor axis is 1.00000011astronomical units.

(a) Write a Cartesian equation for Earth’s orbit.

(b) Give a polar coordinate equation for Earth’s orbit, assuming that the sun is the focus of the elliptical orbit.

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.

foci(±5,1), major axis6

In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.

y=x+1

Use polar coordinates to graph the conics in Exercises 44–51.

r=21-3cosθ

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.

foci(±1,0),major axis4
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