convert the equation to polar co-ordinates (follow-up)

TheBit

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From this 2011 thread:

If there is such a "short cut", forget it. Learn to use algebra. Really.

Could one of you walk me through the first step? How is he able to do that?
 
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From this 2011 thread:

If there is such a "short cut", forget it. Learn to use algebra. Really.

Could one of you walk me through the first step? How is he able to do that?
The post you quoted did not contain any "steps". Please reply with a complete listing of your own efforts, clearly specifying at which "step" you are getting stuck. Thank you! ;)
 
I think the step you're having trouble understanding is the same one that 81ttopcoupe was having trouble understanding back in 2011 - that being the first step in Subhotosh Khan's post. If that's not right, please correct me. The equation in question says:

\(\displaystyle r \cdot sin(\theta)=r^2 \cdot cos^2(\theta)\)

Both sides have an r term, so what if you divide by r?

\(\displaystyle sin(\theta)=r \cdot cos^2(\theta)\)

Now, how would you solve the above equation for r?
 
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