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Introduction to Points, Vectors, And Functions - At A Glance:

Say you want a piece of a pizza, but you don't want the crust. The crust gets stuck in between your teeth, and you have a dentist appointment right after lunch.

The pizza has a 6 inch radius with the crust, but the crust is 1/2 inch thick. When you order your slice, you ask for a slice with only the inner 5 1/2 inches in radius. You receive an odd look from the guy behind the counter, but you are given your pizza sans crust.

Like crustless pizza, there are certain situations that are easier to describe with polar inequalities than with rectangular inequalities. Sometimes giving bounds for r and θ is easier than giving bounds for x and y.

Of course we can also go the other way around, starting with inequalities and ending up with a picture.

Example 1

Write inequalities for r and θ describing the shaded region.

PICTURE polar ineqs 1


Example 2

Write inequalities for r and θ describing the shaded region. 

PICTURE polar ineqs 4


Example 3

Sketch the region described by the inequalities π ≤ θ ≤ 2 π 1 ≤ r ≤ 2.


Example 4

Sketch the region described by the inequality r>2.


Exercise 1

Write inequalities for r and θ describing the given region.

  • PICTURE polar ineqs 6 without pink

Exercise 2

Write inequalities for r and θ describing the given region.

  • PICTURE polar ineqs 7

Exercise 3

Write inequalities for r and θ describing the given region.

  • PICTURE polar ineqs 8

Exercise 4

Sketch the region described by the given inequalities.

  • $π ≤ θ ≤ \frac{3π}{2}$

Exercise 5

Sketch the region described by the given inequalities.

  • r < 4

Exercise 6

Sketch the region described by the given inequalities.

  • \frac{11&pi;}{6}&le; &theta; &le; 2&pi; and 2&le; r &le; 5
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