find the maximum value of:
5+sinx-3cosx and state the value of x for which this maximum occurs
y = 5 + sin x - 3 cos x
dy/dx = 0 at min or max = cos x + 3 sin x
cos x = - 3 sin x
tan x = -1/3
x = -18.4 deg
that is in quadrants 2 and 4
x = 161.6 and 341.6 degrees
at 161.6
5 + sin x -3 cos x =5.27
at 341.6
5 + sin x -3 cos x = 4.64
looks like at 161.6 degrees for max