How do I convert the rectangular equation: x=15 to a polar equation that expresses r in terms on theta?I got r=15 sectheta but wanted to double check

Question

asked Sep 1, 2023 207k views

1 Answer

Smogg · Answer 1 · 2023-09-07T13:39:08+0000

In polar coordinates, the x variable is given as

$x=r\cos \theta$

So, we have the equation

$r\cos \theta=15$

By dividing both sides by cosine of thetat, we get

$r=(15)/(\cos \theta)$

since

$\sec \theta=(1)/(\cos \theta)$

The above result is equivalent to:

$r=15\sec \theta$