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)

Algebra ->  Trigonometry-basics -> 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)      Log On


   

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) About Me  (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:
tan%28B-A%29=%28tanB-tanA%29%2F%281%2BtanA%2AtanB%29
..
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%28B-A%29=%28tanB-tanA%29%2F%281%2BtanA%2AtanB%29
tan%28B-A%29=%28-5%2F12-4%2F3%29%2F%281%2B4%2F3%2A-5%2F12%29
tan%28B-A%29=%28-5%2F12-16%2F12%29%2F%281-20%2F36%29
tan%28B-A%29=%28-21%2F12%29%2F%2816%2F36%29
tan(B-A)≈-3.94
..
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)≈3.9375