SOLUTION: find the exact value of the trigonometric function, cos(u+v), given that sinu=5/13 and cos=-3/5

Algebra ->  Trigonometry-basics -> SOLUTION: find the exact value of the trigonometric function, cos(u+v), given that sinu=5/13 and cos=-3/5       Log On


   



Question 852857: find the exact value of the trigonometric function, cos(u+v), given that sinu=5/13 and cos=-3/5

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the exact value of the trigonometric function,
cos(u+v) = cos(u)cos(v)-sin(u)sin(v)
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sin(u) = 5/13
cos[sqrt(13^2-5^2)]/13 = 12/13
Note: This implies that u is in QI
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cos(v) = -3/5
sin(v) = sqrt(25-9)/5 = 4/5
Note: This implies that v is in QII
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cos(u+v) = cos(u)cos(v)-sin(u)sin(v)
= (12/13)(-3/5) - (5/13)(4/5)
======
= (-36 - 20)/65
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= -56/65
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= -0.8615
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Cheers,
Stan H.
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