Find the exact value of the trigonometric function

Question

Find the exact value of the trigonometric function given that sin(u)=12/13 and cos(v)=-4/5 (Both u and v are in Quadrant II).

cos(u-v)=?

Answer 1

Since sinu = 12/13 and u lies in Q II, cosu = -5/13

Since cosv = -4/5 and v lies in Q II, sinv = 3/5

 

cos(u-v) = cosucosv + sinusinv

 

            = (-5/13)(-4/5) + (12/13)(3/5) = 20/65 + 36/65 = 56/65