SOLUTION: Find the exact value of the trigonometric function given that sin u = 5/13 and cos v = -3/5 (Both are in Quadrant II.) sec (v - u)

We have to pause here and use an identity:



we use it to find cos(u) from sin(u):







Multiply through by 169



Subtract 25 from both sides:









We can determine which sign + or - to use because
we know that both are in Quadrant II, and the
cosine is negative in quadrant II.  So 

we can now substitute that in 





But we still need sin(v).  So we go back to the identity:



we use it to find sin(v) from cos(v):



  



Multiply through by 25



Subtract 9 from both sides:









As before we can determine which sign + or - to use because
we know that both are in Quadrant II, and the sine is
positive in quadrant II.  So 

we can now substitute that in 




Answer: 

Edwin

This is a 5-12-13 Pythag triple, so:  --- cos is < 0 in the 2nd quadrant





This is a 3-4-5 Pythag triple, so:  -------- sin is > 0 in the 2nd quadrant



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