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Chapter 4: Problem 1

Find the equation of the line in the \(x y\) -plane that goes through the origin and makes an angle of 0.7 radians with the positive \(x\) -axis.

Short Answer

Expert verified
The equation of the line that goes through the origin and makes an angle of 0.7 radians with the positive x-axis is \(y \approx 0.842x\).

Step by step solution

01

Find the slope of the line

Recall the definition of slope, which is the tangent of the angle with the positive x-axis. So, let's find the tangent of the given angle: \[ m = \tan(0.7\text{ radians}) \] Using a calculator, we get \(m \approx 0.842\).
02

Use point-slope form to find the equation

Since we know that the line passes through the origin (0, 0) and has a slope of approximately 0.842, we can use the point-slope form to find the equation of the line: The point-slope form of a line is: \[ y - y_1 = m(x - x_1) \] Plugging in the values of our point (0, 0) and our slope (\(m \approx 0.842\)), we have: \(y - 0 = 0.842(x - 0)\)
03

Simplify the equation

Now, let's simplify the equation to get the final result: \[ y = 0.842x \] So, the equation of the line that goes through the origin and makes an angle of 0.7 radians with the positive x-axis is \(y \approx 0.842x\).

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Most popular questions from this chapter

Find exact expressions for the indicated quantities. \(\cos (u-3 \pi)\)

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.] \(\cos \frac{17 \pi}{8}\)

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Explain why $$|\cos (x+n \pi)|=|\cos x|$$ for every number \(x\) and every integer \(n\).
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