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loss tangent is basically a number which how "resistive" is the reactive element and dissipation factor refers much loss would result. As is evident they related nonlinearly. Mainly for capacitors.
Hope this helps
""Dissipation Factor
The dielectric loss angle of an insulating material is the angle by which the phase difference between applied voltage and resulting current deviates from p/2 rad, when the dielectric of the capacitor consists exclusively of the dielectric material. The dielectric dissipation factor tan d of an insulating material is the tangent of the loss angle d. In a perfect dielectric, the voltage wave and the current are exactly 90° out of phase. As the dielectric becomes less than 100% efficient, the current wave begins to lag the voltage in direct proportion. The amount the current wave deviates from being 90° out of phase with the voltage is defined as the dielectric loss angle. The tangent of this angle is known as the loss tangent or dissipation factor.""
When representing the electrical circuit parameters as vectors in a complex plane, known as phasors, a capacitor's dissipation factor is equal to the tangent of the angle between the capacitor's impedance vector and the negative reactive axis, as shown in the diagram to the right. This gives rise to the parameter known as the loss tangent δ.
and tangent δ = DF (dissipation factor).
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