Ok, well, with an alternating current circuit, you know that your ##\omega## values will always be constant when running between current and voltage, so that's pretty helpful. Also, it looks like you are mentioning complex reactance, so you should be able to use Euler's formula to help you solve this problem pretty easily.
http://en.wikipedia.org/wiki/Euler's_formula
(If you don't know this formula, get very handy with it if you are studying circuits)
So, using this information, I assume you already know the equation for the current over a capacitor.
$$ I = C \frac{dV}{dt}$$
And this is all you need in order to solve this problem. Euler's Formula and the equation for current over a capacitor.
Theoretically, the voltage/current in a circuit is defined as the real portion of Euler's formula, which is why the cosine function is always used. So, if you are given a function in terms of just the cosine function, you can rewrite this using Euler's formula, keeping in mind that there is an "imaginary" portion of current that flows through a circuit.
So, say your voltage takes the form $$V(t) = V_{m}\cos(\omega t + \phi)$$
You can actually rewrite this in terms of Euler's formula as $$V_{m}e^{\jmath (\omega t +\phi)}$$
From here, you know how to separate variables in an exponent I'm sure. You should try to use this voltage value to now plug into the formula for the current of a capacitor. You'll notice that, after taking your derivatives and separating your exponents, the part of your equation that is $$V_{m}e^{\jmath \omega t}$$ is actually going to cancel.
In circuits, this is known as solving your problem in the "frequency domain" because your equations are no longer time dependent. This is the underlying principle of using phasor currents and voltages.
Now, impedance is defined as having two parts: the real part and the complex part. The real part is called resistance, and the complex part is called reactance, which I imagine you've learned. In this circuit, you'll notice you only have reactance. Typically, your phase angle is the inverse tangent of your reactance divided by your resistance, but you can solve for your phase angle in this circuit by using the method I outlined above.
Just keep in mind that the imaginary number ##\jmath## is the same thing as $$e^{\jmath \frac{\pi}{2}}$$ and by using simple algebra to simplify your exponents, you can solve for your phase angle, the magnitude of you impedance, and for both the function of your voltage and current.