SOLUTION: If {{{ log(sinx, cosx) = 1/2 }}}, and 0 < x < pi/2, compute sin x.
Algebra.Com
Question 1112839: If , and 0 < x < pi/2, compute sin x.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ \frac{1}{2})
where 
Start with the definition of the logarithm function:
\ =\ y\ \Leftrightarrow\ b^y\ =\ x)
Hence,
\ =\ \cos x)
\ =\ \cos^2(x))
\ =\ 1\ -\ \sin^2(x))
\ +\ \sin(x)\ -\ 1\ =\ 0)
Let )
Substitute back, recalling that the sine function is positive in the first quadrant:
\ =\ \frac{\sqrt{5}\ -\ 1}{2})
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
solve sin^2 x + (sinx)(cosx) =... (answered by Alan3354)
If 0 < x < 90 and {{{ cos x = 3/sqrt (10) }}}, compute... (answered by solver91311,greenestamps)
Verify the reduction formula:
a) sin(x - 5pi/2)= -cosx
b) sin(x+ pi)=... (answered by lwsshak3)
solve cosx(sinx-1/2)=0... (answered by Tatiana_Stebko,oadeshina)
Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and... (answered by lwsshak3)
Please Verify,
'
(1 + sinx - sin^2 x)
-------------------- = (cosx + tanx)
(cosx)
(answered by lwsshak3)
Sin²x+Cos²=1,sinx+cosx=2,solve simultaneously cosx and sinx
(answered by Alan3354)
sinx + cosx - sinxcosx = sin^2 x + cos^2... (answered by Nate)
simplify:
SIN^2 x - COS^2 x/SINX +... (answered by lwsshak3)