SOLUTION: Find the exact value of sin theta, given tan theta < 0 and cos theta =2/9 Could you please show me step by step? I am just not getting this. :(

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of sin theta, given tan theta < 0 and cos theta =2/9 Could you please show me step by step? I am just not getting this. :(      Log On


   

Question 959889: Find the exact value of sin theta, given tan theta < 0 and cos theta =2/9
Could you please show me step by step? I am just not getting this. :(
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of sin theta, given tan theta < 0 and cos theta =2/9
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Use the Pythagorean Identity
sin%5E2%28t%29+%2B+cos%5E2%28t%29+=+1
sin%5E2%28t%29+=+1+-+%284%2F81%29+=+77%2F81
|sin(t)| = sqrt%2877%29%2F9
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cos + and tan negative --> Q4
sine is neg in Q4
--> sin(t) = -sqrt(77)/9