SOLUTION: If {{{ log(sinx, cosx) = 1/2 }}}, and 0 < x < pi/2, compute sin x.

Algebra ->  Trigonometry-basics -> SOLUTION: If {{{ log(sinx, cosx) = 1/2 }}}, and 0 < x < pi/2, compute sin x.      Log On


   

Question 1112839: If +log%28sinx%2C+cosx%29+=+1%2F2+, and 0 < x < pi/2, compute sin x.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




where

Start with the definition of the logarithm function:



Hence,









Let







Substitute back, recalling that the sine function is positive in the first quadrant:



John

My calculator said it, I believe it, that settles it