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Chapter 6: Problem 21

Find the inclination \(\theta\) (in radians and degrees) of the line passing through the points. \((-\sqrt{3},-1),(0,-2)\)

Short Answer

Expert verified
The inclination of the line that passes through the points (-\sqrt{3},-1) and (0,-2) is \(\theta_{rad} = atan(\frac{-2 - (-1)}{0 - (-\sqrt{3})})\) radians and \(\theta_{deg} = \theta_{rad} * \frac{180}{\pi}\) degrees.

Step by step solution

01

Compute the Slope of the Line

First, calculate the slope \(m\) of the line that passes through the points \(-\sqrt{3}, -1\), and \(0, -2\). The calculation is \(m = \frac{y2 - y1}{x2 - x1} = \frac{-2 - (-1)}{0 - (-\sqrt{3})}\).
02

Calculate the Inclination in Radians

Next, calculate the inclination angle in radians (\(\theta_{rad}\)). The inclination angle is the arc-tangent of the slope: \(\theta_{rad} = atan(m) = atan(\frac{-2 - (-1)}{0 - (-\sqrt{3})})\). Remember that atan is the arctangent function, which returns the angle whose tangent is the given number.
03

Convert Inclination to Degrees

Convert the inclination from radians to degrees (\(\theta_{deg}\)). Multiply \(\theta_{rad}\) by \(\frac{180}{\pi}\) to obtain \(\theta_{deg}\). Remember, \(\pi\) radians is 180 degrees, so divide by \(\pi\) and multiply by 180 to change units.

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