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Chapter 6: Problem 25

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

Short Answer

Expert verified
The inclination of the line passing through the points \((\sqrt{3}, 2),(0,1)\) is -\(\pi / 3\) radians or -60 degrees.

Step by step solution

01

Calculate the Slope

First calculate the slope (m) of the line. The formula for the slope is \(m = (y2 - y1) / (x2 - x1)\), where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given points, we get \(m = (1- 2) / (0 - \sqrt{3})\). Solve this to get the value of m.
02

Find the Inclination in Radians

The inclination of the line, \(\theta\), is equal to \(\arctan(m)\). So, substitute \(m\) into \(\theta = \arctan(m)\) and solve for \(\theta\).\)
03

Convert to Degrees

To convert radians to degrees, use the formula \(Degrees = \theta * 180 / \pi\). Substitute the value of \(\theta\) from step 2 and compute the degrees. Round to two decimal places if necessary.

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Most popular questions from this chapter

A straight road rises with an inclination of 0.20 radian from the horizontal. Find the slope of the road and the change in elevation over a one-mile stretch of the road.

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