SOLUTION: given sinu=12/13, sinv=3/5 and cosu>0, find sin (u-v)

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Question 285554: given sinu=12/13, sinv=3/5 and cosu>0, find sin (u-v)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28u%29=12%2F13
You know that
%28sin%28x%29%29%5E2%2B%28cos%28x%29%29%5E2=1
So then
%28sin%28u%29%29%5E2%2B%28cos%28u%29%29%5E2=1
%2812%2F13%29%5E2%2B%28cos%28u%29%29%5E2=1
144%2F169%2B%28cos%28u%29%29%5E2=1
%28cos%28u%29%29%5E2=1-144%2F169
%28cos%28u%29%29%5E2=169%2F169-144%2F169
%28cos%28u%29%29%5E2=25%2F169
cos%28u%29=5%2F13
Similarly for v,
%28sin%28v%29%29%5E2%2B%28cos%28v%29%29%5E2=1
%283%2F5%29%5E2%2B%28cos%28v%29%29%5E2=1
9%2F25%2B%28cos%28v%29%29%5E2=1
%28cos%28v%29%29%5E2=25%2F25-9%2F25
%28cos%28v%29%29%5E2=16%2F25
cos%28u%29=0+%2B-+4%2F5
Unfortunately you don't have any additional information about cos(u), whether it's positive or negative.
Then from trigonmetry,
sin%28u-v%29=sin%28u%29cos%28v%29-cos%28u%29sin%28v%29
sin%28u-v%29=%2812%2F13%29%280+%2B-+4%2F5%29-%285%2F13%29%283%2F5%29
sin%28u-v%29=-%281%2F39%29+%2B-+%2848%2F65%29