Find sin (x + y)

Angle x is acute, angle y is obtuse, cos x = 15/17
and sin y = 3/5. Find sin (x + y).

After doing the math, I found sin (x + y) to be 77/85.

The textbook tells me that the answer is 13/85.

I know 13/85 would be the answer if we were looking for
sin (x MINUS y), right?

sin(x+y) = sin(x)cos(y) +sin(y)cos(x)

Since angle y is a second quadrant angle cos(y)< 0 so you use cos(y) = -4/5 instead of 4/5

sin(x+y) = (-32+45)/85

Quote:

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Originally Posted by Calculus26

sin(x+y) = sin(x)cos(y) +sin(y)cos(x)

Since angle y is a second quadrant angle cos(y)< 0 so you use cos(y) = -4/5 instead of 4/5

sin(x+y) = (-32+45)/85

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I now see what I did wrong. Thanks.