haleyelizabeth2017
  • haleyelizabeth2017
If sin theta=3/5 and theta has its terminal side in Quadrant II, find the exact value of tan 2 theta.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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haleyelizabeth2017
  • haleyelizabeth2017
So would this just be tan(2 theta)=2*sin(theta)*tan(theta)?
haleyelizabeth2017
  • haleyelizabeth2017
Or am I going about this wrong?
jim_thompson5910
  • jim_thompson5910
if it were sin(2theta), then you'd be correct

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jim_thompson5910
  • jim_thompson5910
look at this pdf http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
jim_thompson5910
  • jim_thompson5910
look at the `Double Angle Formulas` on page 2
haleyelizabeth2017
  • haleyelizabeth2017
Oh LOL
haleyelizabeth2017
  • haleyelizabeth2017
I know that tan would be 3/4...So, I just plug that in for theta?
jim_thompson5910
  • jim_thompson5910
you replace every `tan(theta)` with 3/4
haleyelizabeth2017
  • haleyelizabeth2017
I'm confused...so the numerator would just be 2(3/4)?
haleyelizabeth2017
  • haleyelizabeth2017
or 2tan(3/4)?
jim_thompson5910
  • jim_thompson5910
\[\Large \tan(2\theta) = \frac{2\tan(\theta)}{1-\tan^2(\theta)}\] \[\Large \tan(2\theta) = \frac{2\tan(\theta)}{1-(\tan(\theta))^2}\] \[\Large \tan(2\theta) = \frac{2*({\color{red}{\tan(\theta)}})}{1-({\color{red}{\tan(\theta)}})^2}\] \[\Large \tan(2\theta) = \frac{2*({\color{red}{3/4}})}{1-({\color{red}{3/4}})^2}\] \[\Large \tan(2\theta) = ???\]
haleyelizabeth2017
  • haleyelizabeth2017
Ohhh
haleyelizabeth2017
  • haleyelizabeth2017
(3/2)/(1-(9/16)) right?
jim_thompson5910
  • jim_thompson5910
yes, now simplify as much as possible
haleyelizabeth2017
  • haleyelizabeth2017
Okay
haleyelizabeth2017
  • haleyelizabeth2017
24/7?
jim_thompson5910
  • jim_thompson5910
I'm getting the same
jim_thompson5910
  • jim_thompson5910
actually hold on
jim_thompson5910
  • jim_thompson5910
I'm just realizing that theta is in Q2
jim_thompson5910
  • jim_thompson5910
tangent is negative in Q2
haleyelizabeth2017
  • haleyelizabeth2017
so -24/7? LOL
jim_thompson5910
  • jim_thompson5910
correct
haleyelizabeth2017
  • haleyelizabeth2017
Awesome, again, thank you for the help!
jim_thompson5910
  • jim_thompson5910
glad to be of help
haleyelizabeth2017
  • haleyelizabeth2017
:)

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