If tan x = .76 and cos x = .22, what is sin x?

Chris is completely correct.

If tan x = 0.76 then cos x must equal

 $$cosx\approx \pm \frac{100}{125.6}\\


cosx\approx \pm 0.7962$$

Therefore the question is nonsense

See diagram.

$$tan x\times cosx =\frac{sinx}{cosx}\times cos x = sinx\\\\

sinx=0.76\times 0.22$$

 $${\mathtt{0.76}}{\mathtt{\,\times\,}}{\mathtt{0.22}} = {\frac{{\mathtt{209}}}{{\mathtt{1\,250}}}} = {\mathtt{0.167\: \!2}}$$

 So $${\mathtt{sinx}} = {\mathtt{0.167\: \!2}}$$

This was my first thought but as Chris points out it is not correct because the question is nonsense.

If tanx = 0.76 then cosx CANNOT equal 0.22

Thanks Chris!

I believe that this question is nonsensical.......

Consider that tan^-1 (.76) = 37.234833981575°

And cos-1 (.22) = 77.29096700560°

And using the "identity" 

tan (x) * cos(x) = sin(x) , we get

.76 * .22 = .1672

Which means that sin(x) = .1672

And sin^-1 (.1672) = 9.625060859216°

Which leads to the strange "identity" that

tan 37.234833981575° =   sin 9.625060859216° / cos 77.29096700560°

Which, in fact, IS true, if we're willing to let "x" represent three different things at once !!