Question 925334
Evaluate:
sin(x + y) if sin x =3/5, sec x > 0, cos y = &#8722; 2&#8730;(5)/5, and tan y < 0
sin(x + y) =
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sinx=3/5
secx>0
reference angle x is in quadrant I where sin>0, cos>0
cosx=4/5 (working with (3-4-5) reference right triangle in quadrant I)
...
cosy=-2&#8730;5/5
tany<0
reference angle y is in quadrant II where sin>0, cos<0
siny=&#8730;(1-cos^2(y))=&#8730;(1-20/25)=&#8730;(5/25)=&#8730;5/5
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sin(x+y)=sinxcosy+cosxsiny=3/5*-2&#8730;5/5+4/5*&#8730;5/5=-6&#8730;5/25+4&#8730;5/25=-2&#8730;5/25
..
Check:
sinx=3/5
x&#8776;36.87&#730;
cosy=-2&#8730;5/5
y&#8776;153.43&#730;
x+y&#8776;190.30&#730;
sin(x+y)&#8776;sin(190.30)&#8776;-0.1788
exact value as computed=-2&#8730;5/25&#8776;-0.1788