Find the exact value of the trigonometric expression when sin(u) = − 12/13 and cos(v) = − 15/17 . (Both u and v are in Quadrant III.) cos(u + v)

Answer 1

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Answer 2

cos(u) = sqrt (1 - sin²(u)) = -5/13 (-ve sign as cos is neg in Q3)

sin(v) = sqrt (1 - cos²(u)) = -8/17 (-ve sign as sin is neg in Q3)

Now evaluate cos (u + v) with the below formula

cos(u + v) =cos(u)cos(v) - sin(u)sin(v) = (-5/13)(-15/17) - (-12/13)(-8/17) = -(21/221) (u + v will be in Q2 and cos is -ve in the Q2)

hope this helps