Chapter 9: Q. 11 (page 730)

Explain why the inequalities $r > 0$ and $0 < θ < \frac{π}{2}$ 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 $r > 0$ and $π < θ < \frac{3 π}{2}$

Step by step solution

Given information

The inequalities $r > 0$ and $0 < θ < \frac{π}{2}$

Simplification

Consider the inequalities $r > 0$ and $0 < θ < \frac{π}{2}$ .

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

In the first quadrant, all the values are more than $0 °$ and less than $\frac{π}{2}$ .

All the angles are positive in the first quadrant.

Every point $(r, θ)$ lies on the ray since $r > 0$ .and the $θ$ values are in between role="math" localid="1652103013215" $0^{ο} t o \frac{π}{2}$ .

In the third quadrant $r > 0$ and all the $θ$ values are in between $π$ to $\frac{3 π}{2}$ .

Every point $(r, θ)$ lies on the ray and $θ$ values are in between $π$ to $\frac{3 π}{2}$ .

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

$r > 0$ and $π < θ < \frac{3 π}{2}$

Therefore, the answer is $r > 0$ and $π < θ < \frac{3 π}{2}$

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Explain why the inequalities $r > 0$ and $0 < θ < \frac{π}{2}$ together describe the points in the first quadrant. Use similar inequalities to describe the points in the third quadrant.

Short Answer

Step by step solution

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Simplification

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Explain why the inequalities r>0and 0<θ<π2 together describe the points in the first quadrant. Use similar inequalities to describe the points in the third quadrant.

Short Answer

Step by step solution

Given information

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Explain why the inequalities $r > 0$ and $0 < θ < \frac{π}{2}$ together describe the points in the first quadrant. Use similar inequalities to describe the points in the third quadrant.