Question 1007348
cos(u) = 5/13
sin(u) = -12/13 (found from the pythagorean theorem)
angle u is in quadrant 4


Use <a href = "http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf">this page</a> to look at the identities used. In this case, I'm going to use these two identities


sin(x - y) = sin(x)cos(y) - cos(x)sin(y)
cos(x - y) = cos(x)cos(y) + sin(x)sin(y)


those identities are found in the "Sum and Difference Formulas" section on page 2 of the reference sheet.


-----------------------------------------------------


sin(u - pi) = sin(u)cos(pi) - cos(u)sin(pi)
sin(u - pi) = sin(u)(-1) - cos(u)(0)
sin(u - pi) = -sin(u)
sin(u - pi) = -(-12/13)
sin(u - pi) = 12/13


-----------------------------------------------------


cos(u - pi) = cos(u)*cos(pi) + sin(u)*sin(pi)
cos(u - pi) = cos(u)*(-1) + sin(u)*0
cos(u - pi) = -cos(u)
cos(u - pi) = -5/13


-----------------------------------------------------


sin(u - pi/2) = sin(u)cos(pi/2) - cos(u)sin(pi/2)
sin(u - pi/2) = sin(u)(0) - cos(u)(1)
sin(u - pi/2) = -cos(u)
sin(u - pi/2) = -5/13


-----------------------------------------------------


cos(u - pi/2) = cos(u)*cos(pi/2) + sin(u)*sin(pi/2)
cos(u - pi/2) = cos(u)*(0) + sin(u)*1
cos(u - pi/2) = sin(u)
cos(u - pi/2) = -12/13