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Chapter 9: Q. 11 (page 730)

Explain why the inequalities r>0and 0<胃<蟺2 together describe the points in the first quadrant. Use similar inequalities to describe the points in the third quadrant.

Short Answer

Expert verified

The answer is r>0and 蟺<胃<3蟺2

Step by step solution

01

Given information

The inequalities r>0and 0<胃<蟺2

02

Simplification

Consider the inequalities r>0and 0<胃<蟺2.

The objective is to write the inequality which is in the third quadrant.

In the first quadrant, all the values are more than 0掳and less than 蟺2.

All the angles are positive in the first quadrant.

Every point (r,胃)lies on the ray since r>0.and the 胃values are in between role="math" localid="1652103013215" 0慰to蟺2.

In the third quadrant r>0and all the 胃values are in between 蟺to 3蟺2.

Every point (r,胃)lies on the ray and 胃values are in between 蟺to 3蟺2.

Thus, representation of angles by using inequality is as follows,

r>0and 蟺<胃<3蟺2

Therefore, the answer is r>0and 蟺<胃<3蟺2

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