SOLUTION: 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)

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)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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
**
Trig Identity:

..
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)
..
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)
..

tan(B-A)≈-3.94
..
Check:
sinA=4/5
A=53.13�
cosB=-12/13
B=157.38�
B-A=157.38-53.13=104.25
tan(B-A)=tan(104.25�)≈3.9375

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