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Chapter 7: Problem 69

Use a graphing utility to graph the polar equation. $$r=\frac{3}{\cos \theta}$$

Short Answer

Expert verified
The graph of the equation \(r = \frac{3}{\cos(\theta)}\) is a vertical line crossing the point at x = 3 in Cartesian coordinates

Step by step solution

01

Conversion from Polar to Cartesian

Convert the polar equation \(r = \frac{3}{\cos(\theta)}\) into Cartesian equation with the relation \(r^2 = x^2 + y^2\) and \(x = r\cos(\theta)\). Substituting these into the polar equation, we get: x = 3.
02

Plotting the Graph

Use a graphing utility to plot the Cartesian equation. The equation 'x = 3' represents a vertical line passing through (3,0) on the x-axis.
03

Final Verification

Ensure that your graph is a vertical line passing through the point (3,0) on the x-axis to verify the success of the translation and the graphing process.

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Most popular questions from this chapter

Explaining the Concepts Describe the test for symmetry with respect to the line \(\theta=\frac{\pi}{2}\)

In Exercises \(77-80,\) convert to polar form and then perform the indicated operations. Express answers in polar and rectangular form. $$ (1+i)(1-i \sqrt{3})(-\sqrt{3}+i) $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm working with a polar equation that failed the symmetry test with respect to \(\theta=\frac{\pi}{2},\) so my graph will not have this kind of symmetry.

In Exercises \(69-76,\) find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex fifth roots of 32

Solve the equation \(2 x^{3}+5 x^{2}-4 x-3=0\) given that \(-3\) is a zero of \(f(x)=2 x^{3}+5 x^{2}-4 x-3\)
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