Question 602898
If tan A = 9/40, A is in the first quadrant, cos B = -4/5, B is in the third quadrant, find the value of cos(A+B)
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Find the cos(A)
Tan = y/x
Plot the point (40,9)
--> hyp = sqrt(40^2 + 9^2) = 41
cos(A) = x/hyp = 9/41
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cos(A + B) = cosA*cosB - sinA*sinB (from Wikipedia)
Find sin(A) and sin(B)
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sin(A) = y/hyp = 40/41
sin(B) = -3/5 in Q3 (it's the 3, 4, 5 triangle)
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cos(A + B) = cosA*cosB - sinA*sinB
= (9/41)*(-4/5) - (40/41)*(-3/5)
= -36/205 + 120/205
= 84/205