SOLUTION: Find sin (s+t) and cos (s+t) where sin(s)=3/5 and sin(t)=-12/13,in quadrant 1 and t in quadrant 3

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Question 741621: Find sin (s+t) and cos (s+t) where sin(s)=3/5 and sin(t)=-12/13,in quadrant 1 and t in quadrant 3
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find sin (s+t) and cos (s+t) where sin(s)=3/5 and sin(t)=-12/13, s in quadrant 1 and t in quadrant 3
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cos%28s%29=sqrt%281-sin%5E2%28s%29%29=sqrt%281-9%2F25%29=sqrt%2816%2F25%29=4%2F5 (in quadrant 1 where cos>0)
cos%28t%29=sqrt%281-sin%5E2%28t%29%29=sqrt%281-144%2F169%29=sqrt%2825%2F169%29=-5%2F13 (in quadrant 3 where cos<0)
..
sin(s+t)=sin(s)cos(t)+cos(s)sin(t)=3/5*-5/13+4/5*-12/13=-15/65-48/65=-63/65
cos(s+t)=cos(s)cos(t)-sin(s)sin(t)=4/5*-5/13-3/5*-12/13=-20/65+36/65=16/65
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Calculator check:
sin(s)=3/5
s≈36.87º
sin(t)=-12/13
t≈247.38
s+t≈284.25º
..
sin(s+t)=sin(284.25º)≈-0.9692..
as computed,-63/65≈-0.9692..
..
cos(s+t)≈cos(284.25º)≈0.2461..
as computed,16/65≈0.2461..