SOLUTION: sin(x+y) if cosx=8/17 and siny= 12/37
Algebra.Com
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..
RELATED QUESTIONS
Will you please help me solve:
0 (answered by Edwin McCravy)
please help me solve this equation: cosx-siny/cosy+sinx + cosy-sinx/cosx+siny ,... (answered by ikleyn)
please help me solve this equation: cosx-siny/cosy+sinx + cosy-sinx/cosx+siny ,... (answered by ikleyn)
please help me solve this equation: cosx-siny/cosy+sinx + cosy-sinx/cosx+siny ,... (answered by Alan3354,ikleyn)
Find the exact value if 0 < x < pi/2 and 0 < y < pi/2 ; sin(x+y) if sin(x) = 3/5 and... (answered by fractalier)
If x is in the first and y is in the second quadrant, sin = 24/25, and sin y = 4/5, find... (answered by Edwin McCravy)
Given that sinx = 3/5 and cosy = 7/25, with x and y both being Quadrant I angles, find... (answered by ikleyn)
If x+y+a+b=π and {{{ sinx/siny=sina/sinb}}} then prove that... (answered by ikleyn)
Limit y-->o dy/dx=y-->o 1/√tanx +√tanx... (answered by ikleyn)