Question 628586
Please help me evaluate this function. 
tan((B)beta-(a)alpha) if sin(a)=4/5 and cos(B)=-12/13 
(alpha in first quadrant) and (beta in second quadrant
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Trig Identity:
{{{tan(B-A)=(tanB-tanA)/(1+tanA*tanB)}}}
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cosB=-12/13=adjacent side/hypotenuse
opposite side=√(13^2-12^2)=√(25)=5
tanB=-5/12 in quadrant II where tan<0 (opposite side/adjacent side)
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sinA=4/5=opposite side/hypotenuse
adjacent side=3 (3-4-5 right triangle)
tanA=4/3 in quadrant I where tan>0 (opposite side/adjacent side)
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{{{tan(B-A)=(tanB-tanA)/(1+tanA*tanB)}}}
{{{tan(B-A)=(-5/12-4/3)/(1+4/3*-5/12)}}}
{{{tan(B-A)=(-5/12-16/12)/(1-20/36)}}}
{{{tan(B-A)=(-21/12)/(16/36)}}}
tan(B-A)&#8776;-3.94
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Check:
sinA=4/5
A=53.13º
cosB=-12/13
B=157.38º
B-A=157.38-53.13=104.25
tan(B-A)=tan(104.25º)&#8776;3.9375