/*! 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 30 Find the inclination \(\theta\) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 30

Find the inclination \(\theta\) (in radians and degrees) of the line. \(\sqrt{3} x-y+2=0\)

Short Answer

Expert verified
The inclination \(\theta\) of the line \(\sqrt{3} x-y+2=0\) is \(\pi/3\) radians or \(60\degree\).

Step by step solution

01

Convert Line Equation to Slope-Intercept Form

Rewrite the equation of the line to the form \(y=mx+c\). Thus, \(\sqrt{3} x-y+2=0\) becomes \(y=\sqrt{3}x-2\). Here, \(m=\sqrt{3}\) is the slope of the line.
02

Calculate the Inclination Angle in Radians

Find the inclination angle in radians by using \(\theta=\arctan(m)\). Substituting \(m=\sqrt{3}\), we get \(\theta=\arctan(\sqrt{3})=\pi/3\) radians.
03

Convert Radians to Degree

To convert the inclination angle from radians to degrees, we use the conversion factor \(180/\pi\). So, \(\theta = \pi/3\) radians becomes \(\theta = (\pi/3) * (180/\pi) = 60\degree\).

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

Find the eccentricity of the ellipse. \(4 x^{2}+3 y^{2}-8 x+18 y+19=0\)

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(x^{2}+4 y^{2}-6 x+20 y-2=0\)

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (卤7,0)\(;\) foci: (卤2,0)

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\)

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertical major axis; passes through the points (0,6) and (3,0)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Statistics

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.