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The deflection v is the displacement in the y direction of any point on the axis of the beam. Because the y axis is positive + upward, the deflection is also positive when upward (when downward, of course it is negative).

Now the slope of the deflection, v', is the first derivative dv/dx of the expression for the deflection v. In geometric terms, the slope is the increment dv in the deflection (as we go from point m1 to point m2) divided by the increment dx in the distance along the xaxis.

Since dv and dx are infinitesimally small, the slope dv/dx is equal to the tangent of the angle of rotation θ. Thus, dv/dx=tanθ and θ=arctan dv/dx.

I hope i was helpful :P :)

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