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Chapter 6: Problem 42

Find the inclination \(\theta\) (in radians and degrees) of the line. $$2 x-6 y-12=0$$

Short Answer

Expert verified
\(\theta_{radians} = \arctan(\frac{1}{3})\), \(\theta_{degrees} = \arctan(\frac{1}{3}) \times \frac{180}{\pi}\)

Step by step solution

01

Rewrite the Equation in Standard Form

The given line equation is already in the standard form \(Ax + By + C = 0\), where \(A = 2\), \(B = -6\), \(C = 12\).
02

Calculate the Angle of Inclination in Radians

Apply the formula \(\theta = \arctan(-A/B) = \arctan(-(-2/6)) = \arctan(\frac{1}{3})\) to calculate the angle of inclination in radians.
03

Convert Radians to Degrees

Convert the result obtained in step 2 from radians to degrees using the formula \(\theta_{degrees} = \theta_{radians} \times \frac{180}{\pi}\).

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Most popular questions from this chapter

In Exercises \(91-116\), convert the polar equation to rectangular form. $$\theta=5 \pi / 3$$

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$y^{3}=x^{2}$$

In Exercises \(117-126\), convert the polar equation to rectangular form. Then sketch its graph. $$r=2 \sin \theta$$

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$x^{2}+y^{2}=a^{2}$$

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$y^{2}=x^{3}$$
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