Use the formal definition for the curve on a surface. It is equal to the absolute value of the derivative of the tangent of the line divided by the magnitude of the arc length.
Use a curve to test the formula and solve for the curvature.
Curve = (1, 3 cos x, -3 cos x)
Compute the tangent for the curve, which equals:
Tangent = (1/10^.5, 3 cos x/10^.5, -3 sin x/10^.5)
Take the derivative of the Tangent
D(Tangent) = (0, - 3 sin x/10^.5, -3 cos x/10^.5)
Take the magnitude of the two curves, which is the sum of the square of each individual term and then the square root of the entire new formula.
Tangent magnitude = (0 + 9/10 sin^2 x+ 9/10 cos^2 x) = 3/10^.5
Arc magnitude = (1 + 9cos^2 x 9 sin^2 x) = 10^.5
Complete the formula for curvature by dividing the two values.
Curve = 3/10^.5/10.5 = 3/10 = .3