1. Given a function f(x,y) at (x0,y0). Find the two angles the directional derivative makes with the x-axis, where the directional derivative is 1. The angles lie in (-pi,pi]. 2. f(x,y) = sec(pi/14)*sqrt(x^2 + y^2) p0 = (6,6) 3. I use the relation D_u = grad(f) * u, where u is the elementary vector <cos(theta),sin(theta)>. grad(f) at (6,6) is <sec(pi/14)/sqrt(2), sec(pi/14)/sqrt(2)> Using these we have D_u = 1 = sec(pi/14)/sqrt(2)*(cos(theta) + sin(theta)) Rearranging: cos(theta) + sin(theta) = sqrt(2) * cos(pi/14) Isolating theta on LHS by using a relevant angle formula: sqrt(2)*cos(theta - gamma) = sqrt(2) * cos(pi/14), where gamma = atan(1). Here, atan(1) can be pi/4 or -3*pi/4. using cos^-1 on L- and RHS. theta = pi/14 + gamma Giving the answers: theta1 = pi/14 + pi/4 = 9*pi/28 theta2 = pi/14 - 3*pi/4 = -19*pi/28 Somehow these angles are incorrect, but I am unable to locate my error in calculating them. Any help in guidance in the right direction will be greatly appreciated.