SOLUTION: Find the value of tan(a-b) if cos a=4/5 sin b=-5/13 270 degrees < a < 360 degrees and 270 degrees < b < 360 degrees

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Question 824912: Find the value of tan(a-b) if cos a=4/5 sin b=-5/13 270 degrees < a < 360 degrees and 270 degrees < b < 360 degrees
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the value of tan(a-b) if cos a=4/5 sin b=-5/13 270 degrees < a < 360 degrees and 270 degrees < b < 360 degrees.
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reference angles a and b in quadrant IV, in which tan<0.
Identity: tan%28a-b%29=%28tan%28a%29-tan%28b%29%29%2F%281%2Btan%28a%29tan%28b%29%29
..
cosa=4/5 (working with a (3-4-5) reference right triangle)
sina=-3/5
tana=sina/cosa=-3/4
..
sinb=-5/13 (working with a (5-12-13) reference right triangle)
cosb=12/13
tanb=sinb/cosb=-5/12
..
tan%28a-b%29=%28-3%2F4-%28-5%2F12%29%29%2F%281%2B%28-3%2F4%29%28-5%2F12%29%29
tan%28a-b%29=%28-3%2F4%2B5%2F12%29%2F%281%2B%2815%2F48%29%29=-16%2F63