If tan theta =12/5 and cos theta =-5/13, then what is sin theta?

- anonymous

If tan theta =12/5 and cos theta =-5/13, then what is sin theta?

- katieb

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- anonymous

- Michele_Laino

hint:
\[\tan \theta = \frac{{\sin \theta }}{{\cos \theta }}\]

- anonymous

i am confused

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## More answers

- anonymous

@Michele_Laino totally missed that. Much simpler than what I was going to do

- anonymous

how do i go on from there

- 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

ok! please continue @peachpi

- anonymous

the answer i got is 12/13

- anonymous

im not sure what i did, is that correct

- anonymous

you should have gotten a negative number

- UsukiDoll

you're missing a negative sign.

- anonymous

so the answer would be -12/13???

- anonymous

yes

- anonymous

i just did the question again and got -5/13..... i am overthinking the problem i think

- anonymous

so the answer is -12/13

- anonymous

|dw:1436185957944:dw|

- 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

wow this is the first time I've done like this to be honest xD

- anonymous

thank you guys!!!!!!

- anonymous

me too. I usually draw it and use the quadrants

- anonymous

you're welcome

- UsukiDoll

same... since sin was negative and cos was negative, I'm assuming that we were in quadrant 3 because tangent is positive.

- anonymous

yes. I was dutifully drawing a picture when michele came in and blew my mind xD

- 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

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

sorry my typing not working tonight xD but quadrant three is 180 degrees-270 degrees and only tangent is positive.

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