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Chapter 6: Problem 40

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

Short Answer

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

Step by step solution

01

Identify A and B

First, identify the coefficients A and B from the given equation \(-2 \sqrt{3} x - 2 y = 0\). Clearly A = \(-2 \sqrt{3}\) and B = \(-2\).
02

Find the slope

Calculate the slope of the line using the formula \(-A/B\). Thus, the slope is \(-(-2 \sqrt{3}/ -2 ) = \sqrt{3}.\) This is the tangent of the inclination angle.
03

Find the inclination in radians

Now, you know that \(\tan(\theta) = \sqrt{3}\). We can use inverse tangent to find the angle in radians. Therefore, \(\theta = \tan^{-1} (\sqrt{3})\). The value is \(\pi/3\) radians.
04

Convert radians to degrees

To convert radians to degrees, multiply by \(\frac{180}{\pi}\). Therefore, the inclination in degrees is \((\pi/3) * (180/\pi) = 60\) degrees.

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Most popular questions from this chapter

True or False? Determine whether the statement is true or false. Justify your answer. The conic represented by the following equation is a parabola. \(r=\frac{6}{3-2 \cos \theta}\)

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