SOLUTION: Let sin s=-2/3, with s in quad. 3 and let cos t=-1/3, with t in quad. 2. Find each of the following. Sin(s+t)

Question 842702: Let sin s=-2/3, with s in quad. 3 and let cos t=-1/3, with t in quad. 2. Find each of the following.
Sin(s+t)

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Let sin s=-2/3, with s in quad. 3 and let cos t=-1/3, with t in quad. 2. Find each of the following.
Sin(s+t)
Identity: sin(s+t)=sin(s)cos(t)+cos(s)sin(t)
sin(s)=-2/3
cos(s)=-√(1-sin^2(s))=-√(1-4/9)=-√(5/9)=-√5/3
cos(t)=-1/3
sin(t)=√(1-cos^2(t))=√(1-1/9)=√(8/9)=√8/3
sin(s+t)=-2/3*-1/3+-√5/3*√8/3
=2/9-√40/9
=(2-√40)/9
..
Calculator check:
sin(s)=-2/3
s≈221.81˚
cos(t)=-1/3)
t≈109.47˚
s+t≈331.28
sin(s+t)=sin(331.38)≈-0.4790
exact value as calculated=(2-√40)/9≈-0.4805
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