SOLUTION: Hi, Im having a tough time with this problem for trigonometry and was hoping someone could help me out. Find the exact value 2). Find cos(A+B) given that cos A=1/3, with A in

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Question 734834: Hi, Im having a tough time with this problem for trigonometry and was hoping someone could help me out.
Find the exact value
2). Find cos(A+B) given that cos A=1/3, with A in quadrant I, and sin B = -1/4, with B in quadrant IV

am I suppose to use the squareroot of 8 and 15 for the sides of the triangles?
Thanks
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
cos(A) = 1/3

cos^2(A) = (1/3)^2

cos^2(A) = 1/9

1 - cos^2(A) = 1 - 1/9

sin^2(A) = 8/9

sin(A) = sqrt(8/9)

sin(A) = sqrt(8)/3 ... angle A is in quadrant I, so sin(A) is positive

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sin(B) = -1/4

sin^2(B) = (-1/4)^2

sin^2(B) = 1/16

1 - sin^2(B) = 1 - 1/16

1 - sin^2(B) = 15/16

cos^2(B) = 15/16

cos(B) = sqrt(15/16)

cos(B) = sqrt(15)/4 ... angle B is in quadrant IV, so cos(B) is positive

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cos(A+B) = cos(A)cos(B) - sin(A)sin(B)

cos(A+B) = (1/3)(sqrt(15)/4) - (sqrt(8)/3)(-1/4)

cos(A+B) = sqrt(15)/12 + sqrt(8)/12

cos(A+B) = ( sqrt(15) + sqrt(8) )/12

So