Question 741621
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(s)=sqrt(1-sin^2(s))=sqrt(1-9/25)=sqrt(16/25)=4/5}}} (in quadrant 1 where cos>0)
{{{cos(t)=sqrt(1-sin^2(t))=sqrt(1-144/169)=sqrt(25/169)=-5/13}}} (in quadrant 3 where cos<0)
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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&#8776;36.87º
sin(t)=-12/13
t&#8776;247.38
s+t&#8776;284.25º
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sin(s+t)=sin(284.25º)&#8776;-0.9692..
as computed,-63/65&#8776;-0.9692..
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cos(s+t)&#8776;cos(284.25º)&#8776;0.2461..
as computed,16/65&#8776;0.2461..