anonymous
  • anonymous
If tan theta =12/5 and cos theta =-5/13, then what is sin theta?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@peachpi
Michele_Laino
  • Michele_Laino
hint: \[\tan \theta = \frac{{\sin \theta }}{{\cos \theta }}\]
anonymous
  • anonymous
i am confused

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anonymous
  • anonymous
@Michele_Laino totally missed that. Much simpler than what I was going to do
anonymous
  • anonymous
how do i go on from there
anonymous
  • anonymous
what @Michele_Laino has posted is an identity for tan. From here you plug in your numbers and solve for sin Θ
Michele_Laino
  • Michele_Laino
ok! please continue @peachpi
anonymous
  • anonymous
the answer i got is 12/13
anonymous
  • anonymous
im not sure what i did, is that correct
anonymous
  • anonymous
you should have gotten a negative number
UsukiDoll
  • UsukiDoll
you're missing a negative sign.
anonymous
  • anonymous
so the answer would be -12/13???
anonymous
  • anonymous
yes
anonymous
  • anonymous
i just did the question again and got -5/13..... i am overthinking the problem i think
anonymous
  • anonymous
so the answer is -12/13
anonymous
  • anonymous
|dw:1436185957944:dw|
UsukiDoll
  • UsukiDoll
\[\tan(\theta)\cos(\theta) = \sin(\theta) \] since we are given 12/5 for tangent and -5/13 for cosine \[\frac{12}{5}(\frac{-5}{13}) = \sin(\theta) \] the 5's cancel and you are left with -12/13
UsukiDoll
  • UsukiDoll
wow this is the first time I've done like this to be honest xD
anonymous
  • anonymous
thank you guys!!!!!!
anonymous
  • anonymous
me too. I usually draw it and use the quadrants
anonymous
  • anonymous
you're welcome
UsukiDoll
  • UsukiDoll
same... since sin was negative and cos was negative, I'm assuming that we were in quadrant 3 because tangent is positive.
anonymous
  • anonymous
yes. I was dutifully drawing a picture when michele came in and blew my mind xD
UsukiDoll
  • UsukiDoll
hmmm the triangle method would've worked too.. because tangent = opposite/adjacent = 12/5 and cosine = adjacent/hypotenuse =- 5/13 |dw:1436186175987:dw| except we have to respect the fact that since cosine is negative we are placed in one of the four quadrants.
UsukiDoll
  • UsukiDoll
yeah I remember have those problems with the triangles like this and the textbook was like one of them is negative so which quadrant are we
UsukiDoll
  • UsukiDoll
sorry my typing not working tonight xD but quadrant three is 180 degrees-270 degrees and only tangent is positive.

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