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Chapter 6: Problem 64

Convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation. $$r \cos \theta=7$$

Short Answer

Expert verified
The rectangular form of the given polar equation \( r \cos \theta = 7 \) is \( x = 7 \). Its graph is a vertical line passing through the point (7,0) on the x-axis.

Step by step solution

01

Understanding polar to rectangular conversion

We know from conversion identities that \( r \cos \theta = x \). Using this identity, we can rewrite the given polar equation \( r \cos \theta = 7 \) in rectangular form.
02

Conversion from polar to rectangular form

Substituting the identity into the equation, we get \( x = 7 \). This is our rectangular equation.
03

Graph the rectangular equation in a rectangular coordinate system

The graph of the equation \( x = 7 \) is a vertical line passing through the point (7,0) on the x-axis. All points on this line satisfy this equation.

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