/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 89 Determine whether the statement ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 89

Determine whether the statement is true or false. Justify your answer. A line that has an inclination greater than \(\pi / 2\) radians has a negative slope.

Short Answer

Expert verified
The statement is true. A line that has an inclination greater than \(\pi / 2\) radians indeed has a negative slope as it lies in the second quadrant relative to the positive x-axis.

Step by step solution

01

Determining the quadrant where the line lie

The positive x-axis is inclined at 0 radian and the negative x-axis is inclined at \(\pi\) radian. When a line is inclined at an angle between \(0\) and \(\pi / 2\) radians, it's in the first quadrant. When the inclination is greater than \(\pi / 2\) but less than or equal to \(\pi\) radians, the line is in the second quadrant. So, a line that has an inclination greater than \(\pi / 2\) radians lies in the second quadrant relative to positive x-axis.
02

Establishing the relationship between quadrant and slope

A line that lies in the second quadrant has a negative slope because as you read from left to right, the line goes downward. In mathematics, this is interpreted as negative slope.
03

Justify the statement

Given the proofs above, we can say that a line that has an inclination greater than \(\pi / 2\) radians indeed has a negative slope. The statement is therefore true.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercises \(23-48\) , sketch the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $$r=\frac{6}{2 \sin \theta-3 \cos \theta}$$

Converting a Polar Equation to Rectangular Form In Exercises \(91-116,\) convert the polar equation to rectangular form. $$r=-2 \cos \theta$$

In Exercises 65-68, use a graphing utility to graph the polar equation and show that the indicated line is an asymptote of the graph. $$\begin{array}{ll}{\text { Name of Graph }} & {\text { Polar Equation }} & {\text { Asymptote }} \\ {\text { conchoid }} & {r=2-\sec \theta} & {x=-1}\end{array}$$

Converting a Polar Equation to Rectangular Form In Exercises \(91-116,\) convert the polar equation to rectangular form. $$r=\frac{1}{1-\cos \theta}$$

Converting a Polar Equation to Rectangular Form Convert the polar equation \(r=\cos \theta+3 \sin \theta\) to rectangular form and identify the graph.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.