SOLUTION: Given that Sin A = 4/5, 0 < A < &#960;/2 and Cos B = -12/13, &#960;< B < 3&#960;/2, find Cos (A - B) a.) -56/65 b.) 56/65

Algebra ->  Trigonometry-basics -> SOLUTION: Given that Sin A = 4/5, 0 < A < &#960;/2 and Cos B = -12/13, &#960;< B < 3&#960;/2, find Cos (A - B) a.) -56/65 b.) 56/65       Log On


   

Question 824857: Given that Sin A = 4/5, 0 < A < π/2 and Cos B = -12/13, π< B < 3π/2, find Cos (A - B)
a.) -56/65 b.) 56/65 c.) 63/65 d.) -63/65
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Given that Sin A = 4/5, 0 < A < π/2 and Cos B = -12/13, π< B < 3π/2, find Cos (A - B)
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Identity: cos(A-B)=cosAcosB+sinAsinB
sinA=4/5 (working with (3-4-5) reference right triangle in quadrant I in which sin and cos>0.
cosA=3/5
..
cosB=-12/13 (working with (5-12-13) reference right triangle in quadrant III in which sin and cos<0.
sinB=-5/13
..
cos%28A-B%29=%28%283%2F5%29%2A%28-12%2F13%29%29%2B%28%284%2F5%29%2A%28-5%2F13%29%29=-56%2F65
ans: a) -56/65