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Chapter 4: Problem 2

Find the equation of the line in the \(x y\) -plane that goes through the origin and makes an angle of 1.2 radians with the positive \(x\) -axis.

Short Answer

Expert verified
The equation of the line in the xy-plane that goes through the origin and makes an angle of 1.2 radians with the positive x-axis is \(y \approx 2.572x\).

Step by step solution

01

Find the tangent of the angle 1.2 radians.

To find the tangent of the angle 1.2 radians, we will simply use the tangent function: \(m = \tan(1.2)\) Using a calculator, we find the value of the tangent: \(m \approx 2.572\)
02

Plug the slope (m) into the equation.

Since we now have the slope, we can plug it into the point-slope form equation of the line which is simplified as \(y=mx\) since the line passes through the origin. \(y = 2.572x\)
03

Write the equation of the line.

Now that we have all the necessary values, we can write the equation of the line as: \(y = 2.572x\) Thus, the equation of the line in the xy-plane that goes through the origin and makes an angle of 1.2 radians with the positive x-axis is \(y = 2.572x\).

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Most popular questions from this chapter

In Exercises 5-38, find exact expressions for the indicated quantities, given that $$\cos \frac{\pi}{12}=\frac{\sqrt{2+\sqrt{3}}}{2} \text { and } \sin \frac{\pi}{8}=\frac{\sqrt{2-\sqrt{2}}}{2}$$ [These values for \(\cos \frac{\pi}{12}\) and \(\sin \frac{\pi}{8}\) will be derived in Examples 3 and 4 in Section 5.5.] \(\cos \left(-\frac{\pi}{8}\right)\)

Find the smallest positive number \(x\) such that $$ (\cos (x+\pi))(\cos x)+\frac{1}{2}=0 $$

Show that $$\cos ^{4} u+2 \cos ^{2} u \sin ^{2} u+\sin ^{4} u=1$$ for every number \(u\).

In Exercises 5-38, find exact expressions for the indicated quantities, given that $$\cos \frac{\pi}{12}=\frac{\sqrt{2+\sqrt{3}}}{2} \text { and } \sin \frac{\pi}{8}=\frac{\sqrt{2-\sqrt{2}}}{2}$$ [These values for \(\cos \frac{\pi}{12}\) and \(\sin \frac{\pi}{8}\) will be derived in Examples 3 and 4 in Section 5.5.] \(\tan \frac{13 \pi}{12}\)

Suppose \(-\frac{\pi}{2}<\theta<0\) and \(\cos \theta=0.1\). Evaluate \(\sin \theta\).
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