Find the exact value of the expression given that secx=3/2, cscy=3 and x and y are in quadrant 1

Question

anonymous · Answer

Oh and the expression is sin (x+y)

anonymous · Answer

you need a bunch of numbers 
you need $\sin(x), \cos(x), \sin(y), \cos(y)$
do yuou know how to find them ?

anonymous · Answer

I know how to find the cos x and siny
but not the others

anonymous · Answer

$$\cos(x)=\frac{2}{3}$$and  you need $\sin(x)$ draw a triangle

anonymous · Answer

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anonymous · Answer

the third side, by pythagoras , is 
$$\sqrt{3^2-2^2}=\sqrt5$$

anonymous · Answer

OOPS!
$$\huge \sin(x)=\frac{\sqrt5}{3}$$ sorry

anonymous · Answer

Ok that makes sense. And you do that similarly to cosy, right? Is cosy=(2sqrt2)/3

anonymous · Answer

yes you do 
idk i didn't do it but i can check real quick

anonymous · Answer

yes you are right

anonymous · Answer

Ok well if that is right I should be able to do the rest. Thank you so much!

anonymous · Answer

yw, "addition angle" formula from here on in
plug in the numbers, see what you get