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Jamierox4ev3r
 one year ago
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Jamierox4ev3r
 one year ago
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Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2Give me a second to type the equation, thanks :)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2Solve: \[2\tan ^{2}\theta \sin \theta  \tan ^{2}\theta=0\] for all values in [0, 360] <degrees

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2@ganeshie8 any ideas?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3it seems \(\tan^2\theta\) is common in both the terms you may start by factoring it out

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2Alright. So that would be \( \tan( 2\tan \theta \sin \theta\tan \theta )\) right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3pull out the entire \(\tan^2\theta\)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2the entire thing? then that would leave you with.. just sine I believe. So \(\tan^{2} \theta (2\sin \theta\theta)\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3wait a sec, \(\tan^{2} \theta (2\sin \theta\color{Red}{\theta})\) are you really sure that \(\color{Red}{\theta}\) stays back there ?

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2wait... no it wouldn't. whoops xD

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\(\tan^2\theta\) is ONE SINGLE thing \(\tan^2\) and \(\theta\) are not two pieces

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2^ yes I recall that now. But wouldn't something have to stay there?

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2oh wait. wouldn't it just be 1?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3good, please fix it also what happened to \(= 0\)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2oh it's still there, I just lopped it off. So as of now, this is where we are. \(\tan^{2} \theta (2\sin \theta1)=0\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3looks good! what are you going to do next

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2I'm not sure....seems to me like there is a trigonometric identity somewhere in there perhaps.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Easy, actually we're almost done! all we need to know is the "zero product property"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1441068917025:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3so far we have : \(\color{red}{\tan^{2} \theta} \color{blue}{(2\sin \theta1)}=0\) By zero product property, \(\color{red}{\tan^2\theta}=0\) or \(\color{blue}{2\sin\theta1}=0\) solve each of them separately using unit circle

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2so we could set either one to zero. And solve for theta \((\theta)\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Exactly! thats what zero product property tells us

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2wow. that actually makes so much sense. Alright, so let me solve each separately and I'll be back with you on what I got

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3take ur time you may have to use unit circle as you're asked to find all the solutions between 0 and 360

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2Alright. So I got that \(\Large\sin \theta = \frac{1}{2}\) So from that, I found that \(\Large\theta = 30 (degrees), 150 (degrees)\)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2I wasn't as sure for \(\tan \theta\), but I think that \(\Large\tan \theta =0\) and from that, wouldn't \(\Large\theta = 0 (degrees)\) ?? **not sure**

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Excellent! \(\tan\theta=0\) should give you 3 solutions

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3il give a hint : \(\tan\theta = \tan(\theta+180)\)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2oh wait i think i see. 90 degrees would be undefined

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3In other words : adding 180 to the angle wont change the value of \(\tan(\theta)\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\(\tan\theta=0\) \(\implies \theta = \{0,\pm 180,\pm 360,\pm540,\ldots\}\) since you want the solutions between 0 and 360 you just pick \(0,180,360\)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2oh and btw, I can include 0 degrees, but not 360. I was supposed to write the problem like [0,360) instead of [0,360]. So technically, for this problem, there are only two solutions that come from \(\tan \theta =0\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Oh then you're absolutely right!

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2alright, so in total, all the solutions are 0, 30, 150, and 180! (all in degrees) oh my goodness, thank you so much! This review material was so distant in my memory, until you came along of course. Your patience is outstanding, thank you

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3np your patience is outstanding too! keep it up :)

Jamierox4ev3r
 one year ago
Best ResponseYou've already chosen the best response.2d'aw you flatter me :')
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