SOLUTION: If sin p= 2/3 and p is greater than 90 and smaller than 180 then what is tan p equal to? Please solve and explain. Thanks

Algebra ->  Angles -> SOLUTION: If sin p= 2/3 and p is greater than 90 and smaller than 180 then what is tan p equal to? Please solve and explain. Thanks       Log On


   

Question 237628: If sin p= 2/3 and p is greater than 90 and smaller than 180
then what is tan p equal to?
Please solve and explain.
Thanks
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If sin p= 2/3 and p is greater than 90 and smaller than 180
then what is tan p equal to?
-------------
If sin(p) = 2/3 , y = 2 and r = 3
Then x = sqrt(r^2-y^2) = sqrt(9-4) = sqrt(5)
----------------------------------------------
tan(p) = ?
tan(p) = y/x
---
Note: y is positive in the 2nd Quadrant and x is negative
---
So you get tan(p) = 2/(-sqrt(5)) = -(2sqrt(5)/5 or (-2/5)sqrt(5)
===============================================================
Cheers,
Stan H.