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Urgent help requested!! Anything I can do to get an answer faster, in terms of my question??

The question, diagram, and my work are attached. Any help or suggestions or hints are extremely welcome and appreciated.

Homework help

image2 My apologies for the tags. I couldn't find one that accurately described the content in this question. Also apologies for the bad title. Doing this on a mobile device and I had too many characters and then it made me wait for 30-60 seconds.

more ideas

More of my ideas.

Jon
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Jeff
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1 Answers1

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the shortest distance to the line from the origin is $$r\cos(\theta - \theta_0) = r_0.$$ you can divide it out and get the polar equation of the line that is distance $r_0$ from the origin is $$r = \frac{r_0}{\cos (\theta- \theta_0)}. $$

abel
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  • Call me stupid but I'm not understanding how $r cos($$\theta$ -$\theta_0$) = $r_0$ – Jeff Mar 05 '15 at 03:48
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    look at the right angle triangle in the figure with the hypotenuse $r$ and $r_0$ the perpendicular line from the origin to the line. the angle between the hypotenuse and this line is $\theta - \theta_0.$ use the formula $\cos = \frac{adj}{hyp}.$ – abel Mar 05 '15 at 03:52