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Chapter 6: Problem 20

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

Short Answer

Expert verified
The inclination of the line passing through the points (1,2鈭�3) and (0, 鈭�3) is \( \theta = \pi/3 \) radians or 60 degrees.

Step by step solution

01

Find the slope of the line

To find the slope (m) of the line, we use the formula \( m = \frac{y2-y1}{x2-x1} \) using the coordinates provided. Thus \( m = \frac{\sqrt{3} - 2\sqrt{3} }{0-1} \) which simplifies to \( m = \sqrt{3} \)
02

Calculate Inclination in Radians

Recalling that the slope of a line is equal to the tangent of the angle it makes with the x-axis, \( tan(\theta)= m = \sqrt{3} \). Given that \( tan(\pi/3) = \sqrt{3} \), it follows that \( \theta = \pi/3 \) radians
03

Calculate Inclination in Degrees

To convert our angle from radians to degrees, we'll use the fact that \( \pi \) radians is equivalent to 180 degrees. Therefore \( \theta = \pi/3 \times \frac{180}{\pi} = 60 \) degrees

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