Second order RLC circuit problem about signs
If: - 

$$\omega_d \sin (\phi) = \alpha\cos(\phi)$$ Then: -

$$\dfrac{\sin (\phi)}{\cos(\phi)} = \dfrac{\alpha}{\omega_d}$$

Or: -

$$\tan(\phi) = \dfrac{\alpha}{\omega_d}$$

Can you take it from here?