Question 699890: sin(x+y) if cosx=8/17 and siny= 12/37
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! sin(x+y) if cosx=8/17 and siny= 12/37
**
A=adjacent side
O=opposite side
H=hypotenuse
..
cos x=8/17
A=8, H=17
O=√(H^2-A^2)
=√(17^2-8^2)
=√(289-64)
=√225
O=15
sin x=O/H=15/17
..
cos x=8/17
A=8, H=17
O=√(H^2-A^2)
=√(17^2-8^2)
=√(289-64)
=√225
O=15
sin x=O/H=15/17
..
sin y=12/37
O=12, H=37
A=√(H^2-O^2)
=√(37^2-12^2)
=√(1369-144)
=√1225
A=35
cos y=A/H=35/37
..
sin(x+y)=sin x cos y+cos x sin y
=15/17*35/37+8/17*12/37
=525/629+96/629
=621/629
..
check: w/calculator
x=cos^-1 (8/17)=61.9275º
y=sin^-1 (12/37)=18.9246
x+y=80.8521º
sin(x+y)=sin(80.8521º)≈0.9872..
621/629≈0.9872..
|
|
|
