Question 1060297
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)
<pre>{{{sin (u) = 5/13}}}
This is a 5-12-13 Pythag triple, so: {{{cos (u) = - 12/13}}} --- cos is < 0 in the 2nd quadrant

{{{cos (v) = (- 3)/5}}}
This is a 3-4-5 Pythag triple, so: {{{sin (v) = 4/5}}} -------- sin is > 0 in the 2nd quadrant

{{{sec (v - u) = 1/cos (v - u) = 1/(cos (v) cos (u) + sin (v) sin (u))}}} ====> {{{1/((- 3/5) * (- 12/13) + (4/5) * (5/13))}}} ======> {{{1/(36/65 + 20/65)}}} ====> {{{highlight_green(1/(56/65) = 65/56)}}}