Question 834804
Find values of sin(a-b)if cos a=15/17, cot b=24/7, 0 degrees<a<90 degress, and 0 degrees< b< 90 degreea.
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{{{sin(a-b)=sin(a)cos(b)-cos(a)sin(b)}}}
cos(a)=15/17
{{{sin(a)=sqrt(1-cos^2(a))=sqrt(1-(225/289))=sqrt(64/289)=8/17}}}
sin(a)=8/17
..
cot(b)=24/7
hypotenuse={{{sqrt(24^2+7^2)=sqrt(24^2+7^2)=sqrt(625)=25}}}
sin(b)=7/25
cos(b)=24/25
..
{{{sin(a-b)=(8/17)(24/25)-(15/17)(7/25)}}}
{{{sin(a-b)=(8/17)(24/25)-(15/17)(7/25)=87/425}}}
..
calculator check:
cos(a)=15/17
a&#8776;28.07&#730;
tan(b)=7/24
b&#8776;16.26&#730;
a-b&#8776;28.07-16.26&#8776;11.81&#730;
sin(a-b)=sin(11.81)&#8776;0.2046..
exact value as calculated=87/425&#8776;0.2047..