Question 861248
Find tan(s+t) if cos s = (-1/5), sin t = 3/5, and s and t are in quadrant 2.
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{{{tan(s+t)=(tan(s)+tan(t))/(1-tan(s)tan(t))}}}
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cos(s)=-1/5
{{{sin(s)=sqrt(1-cos^2(s))=sqrt(1-(1/25))=sqrt(24/25)=sqrt(24)/5}}}
tan(s)=sin/cos=-√24/1=-√24
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sin(t)=3/5 (working with a (3-4-5) reference right triangle in quadrant 2)
cos(t)=-4/5
tan(t)=sin/cos=-3/4
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{{{tan(s+t)=(tan(s)+tan(t))/(1-tan(s)tan(t))}}}
tan(s+t)=(-√24-3/4)/(1-√24*(3/4)
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calculator check:
cos(s)=-1/5
s≈101.54 deg
sin(t)=3/5
t≈143.13
s+t≈244.67
tan(s+t)=tan(244.67)≈2.112…
exact value as calculated=(-√24-3/4)/(1-√24*(3/4)≈2.112...
note: let me know if my solution is correct, helpful and understandable