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infinitemoes
 one year ago
what values for θ(0<θ<2pi) satisfy this equation? tan^2 θ = 3/2 secθ
infinitemoes
 one year ago
what values for θ(0<θ<2pi) satisfy this equation? tan^2 θ = 3/2 secθ

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satellite73
 one year ago
Best ResponseYou've already chosen the best response.1this is a poser, hold on i think i have an idea

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1it is not that hard, just my first attempt didn't work add \(\frac{3}{2}\sec(x)\) to start withi \[\tan^2(x)+\frac{3}{2}\sec(x)=0\] then rewrite as \[\frac{\sin^2(x)}{\cos^2(x)}+\frac{3}{2\cos(x)}=0\] add up to get \[\frac{2\sin^2(x)+3\cos(x)}{2\cos^2(x)}=0\] then set the numerator equal to zero and solve

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1you get \[2\sin^2(x)+3\cos(x)=0\] rewrite as \[2(1\cos^2(x))+3\cos(x)=0\] and solve the quadratic equation in cosine

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1you good from there or you need more steps?

infinitemoes
 one year ago
Best ResponseYou've already chosen the best response.0I'm gonna be honest with ya, I have absolutely no idea what I'm doing. So extra steps would be great!

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1ok but before i write them, do you have any questions about the steps i wrote? there was no real trig, just algebra

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1the only trig i used was that \(\tan^2(x)=\frac{\sin^2(x)}{\cos^2(x0}\) and \(\sec(x)=\frac{1}{\cos(x)}\)

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1now we have \[2(1\cos^2(x))+3\cos(x)=0\] which is like solving \[2(1u^2)+3u=0\] rewrite as \[22u^3+3u=0\] or \[2u^23u2=0\] factor as \[(2u+1)(u2)=0\] so \[u=\frac{1}{2}\] or \[u=2\] i.e. \[\cos(x)=\frac{1}{2}\] which is the only solution, because cosine cannot be 2

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1then look in the unit circle to see for what values of \(x\) you get \[\cos(x)=\frac{1}{2}\] and you will see it is \[x=\frac{2\pi}{3}\] or \[x=\frac{4\pi}{3}\]

infinitemoes
 one year ago
Best ResponseYou've already chosen the best response.0oh my gosh you are wonderful. thank you so much!
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