I'm getting close to the right answer, but one little thing is off. I think I'm missing a negative somewhere...
Here's my work:"Find the exact value for each of the following under the given conditions:
(a) sin(alpha + beta) ... etc...
Sin alpha = 5/13 , -3pi/2 < alpha < -pi ; Tan beta = -sqrt of 3 , pi/2 < beta < pi
I make a couple of pictures to find the missing side. For alpha I get a triangle in quadrant II. I get the missing, base, side is equal to 12 after using the Pythagorean theorem. The 12 is also negative because of the quadrant.
For beta I get another triangle in quadrant II. I get the missing, hypotenuse, side is equal to 2.
I then plug the numbers into the sum and difference formula for Sin(alpha + beta) which is sin alpha cos beta + cos alpha sin beta
I get (5/13) (-1/2) + (-12/13) (sqrt3/2)
= (-5/26) + (-12sqrt3/26)
= -5 - 12sqrt3 all over 26.
The answer should be 5 + 12sqrt3 all over 26.
Where are my negatives coming from? Did I use the wrong quadrant or did I miss something in the work?