SOLUTION: Find the exact value of cos(x-y) if sinx= 4/5 in Quadrant II and tan y=12/5 in Quadrant III I think it uses a double angle or haf angle formula, Im new to this topic and am strugg

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of cos(x-y) if sinx= 4/5 in Quadrant II and tan y=12/5 in Quadrant III I think it uses a double angle or haf angle formula, Im new to this topic and am strugg      Log On


   

Question 961976: Find the exact value of cos(x-y) if sinx= 4/5 in Quadrant II and tan y=12/5 in Quadrant III
I think it uses a double angle or haf angle formula, Im new to this topic and am struggling, Id like a in-depth step by step solution. THanks for your time
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of cos(x-y) if sinx= 4/5 in Quadrant II and tan y=12/5 in Quadrant III
***
sinx=4/5
cosx=-3/5
working with (5-12-13) reference right triangle in quadrant III
siny= -12/13
cosy=-5/13
..
Identity: cos(x+y)=cosxcosy-sinxsiny=-3/5*-5/13-4/5*-12/13=15/65+48/65=63/65
..
Check:
sinx=4/5 (Q2)
x=126.86˚
tany=12/5 (Q3)
y=247.38˚
x+y=374.24˚
cos(x+y)=cos(374.24)≈0.9692..
Exact value as computed above=63/65≈0.9692..