SOLUTION: Given cos(x) = 1&#8260;9 with 0o < x < 90o, and cos(y) = 1&#8260;11 with 270o < y < 360o. Find cos(x + y).

Algebra ->  Trigonometry-basics -> SOLUTION: Given cos(x) = 1&#8260;9 with 0o < x < 90o, and cos(y) = 1&#8260;11 with 270o < y < 360o. Find cos(x + y).      Log On


   

Question 951463: Given cos(x) = 1⁄9 with 0o < x < 90o, and cos(y) = 1⁄11 with 270o < y < 360o. Find cos(x + y).
Answer by lwsshak3(11628) About Me  (Show Source):
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Given cos(x) = 1⁄9 with 0o < x < 90o, and cos(y) = 1⁄11 with 270o < y < 360o. Find cos(x + y).
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cosx=1/9 (Q1)
sinx=√(1-cos(x)^2)=√(1-1/81)=√(80/81)=√80/9
cosy=1/11(Q4)
siny=-√(1-cos(y)^2)=-√(1-1/121)=-√(120/121)=-√120/11
..
cos(x+y)=cosxcosy-sinxsiny=1/9*1/11-√80/9*-√120/11=1/99+√9600/99=(1+√9600)/99
Check:
Cosx=1/9
x≈83.62˚
cosy=1/11
y≈275.22˚
x+y≈358.84˚
cos(x+y)≈cos(358.54)≈0.9997
exact value as computed=(1+√9600)/99≈0.9997