Board 8 > Math people, I have a question (Calculus)

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Anagram 10/27/17 12:54:41 PM #1:	I've puzzled over this for half an hour now, but I'm sure the answer is easy. I can't ask the tutoring center for help because I'm somewhere else today and they're closed on weekends. The question is simple: find a Cartesian equation for the curve (r^2)cos(2theta)=1. I know r^2=x^2+y^2, and I know to use a double angle identity on cos(2theta). My problem is that the double angle identities (1-sin(theta)) and (2cos^2(theta)-1) lead me to x^2=1 and y^2=-1, both of which are obviously not the answer I need. This happens because I end up with something like r^2(1-sin^2(theta)=1, which just gets me r^2-r^2sin^2(theta)=1, and the r^2sin^2(theta) becomes a -y^2, which cancels out the other y^2 and leaves me just an x^2, which isn't helpful. I know the answer will look something like x^2/something + y^2/something = something, but I have no idea how to keep the x^2 and y^2 from disappearing while removing the theta. --- Not changing this sig until I decide to change this sig. Started: July 6, 2005 <cite>Anagram posted [p:889253626] in Math peopl... [t:75925980]...</cite> <quote>I've puzzled over this for half an hour now, but I'm sure the answer is easy. I can't ask the tutoring center for help because I'm somewhere else today and they're closed on weekends. The question is simple: find a Cartesian equation for the curve (r^2)cos(2theta)=1. I know r^2=x^2+y^2, and I know to use a double angle identity on cos(2theta). My problem is that the double angle identities (1-sin(theta)) and (2cos^2(theta)-1) lead me to x^2=1 and y^2=-1, both of which are obviously not the answer I need. This happens because I end up with something like r^2(1-sin^2(theta)=1, which just gets me r^2-r^2sin^2(theta)=1, and the r^2sin^2(theta) becomes a -y^2, which cancels out the other y^2 and leaves me just an x^2, which isn't helpful. I know the answer will look something like x^2/something + y^2/something = something, but I have no idea how to keep the x^2 and y^2 from disappearing while removing the theta.</quote> ... Copied to Clipboard!
Janus5k 10/27/17 1:06:20 PM #2:	cos2t = cos^2-sin^2 --- "Those who cast the vote decide nothing. Those who count the vote decide everything." <cite>Janus5k posted [p:889254316] in Math peopl... [t:75925980]...</cite> <quote>cos2t = cos^2-sin^2</quote> ... Copied to Clipboard!
Anagram 10/27/17 1:11:05 PM #3:	Janus5k posted... cos2t = cos^2-sin^2 So x^2 - y^2 = 1? --- Not changing this sig until I decide to change this sig. Started: July 6, 2005 <cite>Anagram posted [p:889254561] in Math peopl... [t:75925980]...</cite> <quote><cite>Janus5k posted...</cite> <quote>cos2t = cos^2-sin^2</quote> So x^2 - y^2 = 1?</quote> ... Copied to Clipboard!
Anagram 10/27/17 1:21:44 PM #4:	Ah, I got it, thanks. Embarrassing that I used every cos2x identity but the correct one. --- Not changing this sig until I decide to change this sig. Started: July 6, 2005 <cite>Anagram posted [p:889255174] in Math peopl... [t:75925980]...</cite> <quote>Ah, I got it, thanks. Embarrassing that I used every cos2x identity but the correct one.</quote> ... Copied to Clipboard!
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