SOLUTION: Given that angle X is in the first quadrant and cosX = 15/17 and angle Y terminates in the second quadrant (pi/2 < Y < pi) and sin Y = 12/13, then find the value of cos(Y-X) in fra

Algebra ->  Trigonometry-basics -> SOLUTION: Given that angle X is in the first quadrant and cosX = 15/17 and angle Y terminates in the second quadrant (pi/2 < Y < pi) and sin Y = 12/13, then find the value of cos(Y-X) in fra      Log On


   

Question 852241: Given that angle X is in the first quadrant and cosX = 15/17 and angle Y terminates in the second quadrant (pi/2 < Y < pi) and sin Y = 12/13, then find the value of cos(Y-X) in fraction form.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Given that angle X is in the first quadrant and
cosX = 15/17
sin(X) = sqrt(17^2-15^2)/17 = 8/17
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and angle Y terminates in the second quadrant (pi/2 < Y < pi) and
sin Y = 12/13
cos(Y) = -sqrt(13^2-12^2)/13 = -5/13
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then find the value of cos(Y-X) in fraction form.
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cos(y-x) = cos(y)cos(x)+sin(y)sin(x)
= (-5/13)(15/17)+(12/13)(8/17)
= (-75+96)/(13*17)
= (21)/(13*17)
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Cheers,
Stan H.
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