Trigonometric questions

tanθ=sinθ/cosθ
tan^2θ=sin^2θ/cos^2θ
r^2=sin^2θ/(1-sin^2θ)
r^2-r^2sin^2θ=sin^2θ
r^2=sin^2θ(1+r^2)
sin^2θ=r^2/(1+r^2)
sinθ=+/-r/sqrt(1+r^2)

(Using a diagram to respresent the question will be better.)

Given that tanθ=r,
i.e. tanθ=r/1
In the graph, we can say that the opp.side(BC) of θ is r, and
the adj. side(AB) is 1.
From the Pyth. thm.,
we have the hyp.(AC) =±√(1+r^2).

Therefore, we have sinθ=BC/AC=± r/√(1+r^2).

ps. the diagram I drew is:
http://i146.photobucket.com/albums/r254/kwanhimshek/hk_diff_trigo_simplify.jpg

Is θ an acute angle?