SOLUTION: Is sec theta = 12/5 with theta in Quadrant IV, find tan theta.

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Question 1097963: Is sec theta = 12/5 with theta in Quadrant IV, find tan theta.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In quadrant IV, cosine (and secant) are positive,
but,since,and tangent are negative.
sec%28theta%29=1%2Fcos%28theta%29=12%2F5 ---> cos%28theta%29=5%2F12
For all angles, cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1 ,
so %285%2F12%29%5E2%2Bsin%5E2%28theta%29=1 --> 25%2F144%2Bsin%5E2%28theta%29=1 --> sin%5E2%28theta%29=1-25%2F144=%28144-25%29%2F144=119%2F144 ,
and because sin%28theta%29 is a negative number in quadrant IV,
sin%28theta%29=-sqrt%28119%2F144%29=-sqrt%28119%29%2F12 .
Then, because for any angle tan%28theta%29=sin%28theta%29%2Fcos%28theta%29 ,
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