Because we know the state of a qubit can be described as: $$ |q\rangle=\cos{\frac{\theta}{2}}|0\rangle+e^{i\phi}\sin{\frac{\theta}{2}}|1\rangle $$$$ |q\rangle=\cos{\frac{\theta}{2}}|0\rangle+e^{i\phi}\sin{\frac{\theta}{2}}|1\rangle\\\ \\ \theta, \phi \in \mathbb{R} $$
How do I find the values of $\theta$ and $\phi$ when the qubit is in the state below? $$ \frac{1}{\sqrt{2}}\begin{bmatrix}i\\1\end{bmatrix} $$
What I've done so far:
$$ |q\rangle = \frac{i}{\sqrt{2}}|0\rangle + \frac{1}{\sqrt{2}}|1\rangle $$ Therefore $$ \cos{\frac{\theta}{2}} = \frac{i}{\sqrt{2}}\\ e^{i\phi}\sin{\frac{\theta}{2}} = \frac{1}{\sqrt{2}} $$
But I don't know where to go from here. Could anyone give me some guidance?
