Fine each exact value if (π/2)

Question

Fine each exact value if (π/2)<x<π and 0<y<(π/2).

sin(x-y) if sin(y)=(4/5), csc(x)=7

anonymous · Answer

EDIT**

Find not fine

anonymous · Answer

note that $\sin(x-y) =\sin x \cos y - \sin y \cos x$
and $\cos x =\sqrt{1-\sin^2 x}$

anonymous · Answer

do you need further help?

anonymous · Answer

I really could use this done out so I can compare it with another problem.

anonymous · Answer

ah. okaay. so that means you've not done this?
since sin y is given, and 0<y<(π/2), then $\cos y =\sqrt{1-(\frac{4}{5})^2}=\frac{3}{5}$
csc x =7, so sin x=1/7 and cos x (from previous reasoning is $\frac{2\sqrt3}{7}$) sub all to get sin(x-y)

anonymous · Answer

Alright thanks. Just needed to compare with another method to see how it played out.

anonymous · Answer

ah. :) good luck with the other one.

anonymous · Answer

lol  actually there's another way to this. find the angles x and y and subtract.