SOLUTION: If 0 < x < 90 and {{{ cos x = 3/sqrt (10) }}}, compute log(sinx)+log(cosx)+log(tanx).

Algebra ->  Trigonometry-basics -> SOLUTION: If 0 < x < 90 and {{{ cos x = 3/sqrt (10) }}}, compute log(sinx)+log(cosx)+log(tanx).      Log On


   

Question 1112843: If 0 < x < 90 and +cos+x+=+3%2Fsqrt+%2810%29+, compute log(sinx)+log(cosx)+log(tanx).
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Given . Hence, , , and













The rest is just calculator work. I'll leave that to your capable fingers.

John

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

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


log(sinx)+log(cosx)+log(tanx) = log(sinx*cosx*tanx) = log((sinx)^2)

If the angle is in quadrant I and cosx = 3/sqrt(10), then sinx = 1/sqrt(10).

Then log((sinx)^2) = log(1/10) = -1.