/*! 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 passing through the points. $$(12,8),(-4,-3)$$

Short Answer

Expert verified
The angle of inclination in radians is \(atan(-3/4)\) and in degrees is \(atan(-3/4) * 180/\pi\)

Step by step solution

01

Compute the Slope

First, calculate the slope of the line using the provided coordinates. The formula for the slope is \(m=(y2 - y1) / (x2 - x1)\). Here, the points are (12, 8) and (-4, -3), so the slope will be \(((-3 - 8) / (-4 - 12))=-3/4\)
02

Find the Angle of Inclination in Radians

Next, to find the angle of inclination \(\theta\) in radians, one can use the arctangent of the slope. The arctangent in most programming languages and calculators is 'atan' or 'tan^-1'. So the angle in radians would be \(\theta = atan(m) = atan(-3/4)\)
03

Convert Radians to Degrees

To convert radians to degrees, multiply the angle in radians by \(180/\pi\). Consequently, \(\theta\) (in degrees) = \( \theta * 180/\pi\)

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

Think About It \(\quad\) Explain what each of the following equations represents, and how equations (a) and (b) are equivalent. A. \(y=a(x-h)^{2}+k, \quad a \neq 0\) B. \((x-h)^{2}=4 p(y-k), \quad p \neq 0\) C. \((y-k)^{2}=4 p(x-h), \quad p \neq 0\)

In Exercises \(117-126\), convert the polar equation to rectangular form. Then sketch its graph. $$r=-6 \cos \theta$$

Find the distance between the point and the line. Point \((2,3)\) Line \(3 x+y=1\)

Determine whether the statement is true or false. Justify your answer. It is possible for a parabola to intersect its directrix.

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$y=-2$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Geometry

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.