Purple haze
Thought I'd clear up some bad info (bloody long for clarity, sorry in advance for boredom, other instructors please fault-find as I've got an upgrade coming next month
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The induced drag is created by the same mechanism or system that creates wake turbulence, it is not created by wake turbulence itself.
Part of the problem is the way we define lift, i.e. "That part of the total aerodynamic reaction that acts at 90 deg to the relative air flow (RAF)". Hold this thought.
The total aerodynamic reaction around an aerofoil acts slightly behind 90 deg to the RAF (in the direction of the trailing edge).
Now our definition comes into play - with Lift acting at 90 deg to the RAF (by definition), the remaining component of the total reaction acts parallel to the RAF, this is what we call Induced Drag i.e. "Drag" induced by the production of "Lift". Really they are part of the same total reaction, we just label them as separate components to make it easier to add up total drag etc.
Now
the long way
An aerofoil creates lift by creating a difference in pressure between top surface and bottom surface (or one side and the other side of a vertical aerofoil i.e. tailfin). There is slightly higher pressure underneath the aerofoil and proportionately much lower pressure on top. The difference in pressure forces some air to try and escape to the low pressure area on top of the wing, which can frequently happen at the end of the wing where there is no longer a physical barrier to this process. This creates a component of airflow which runs sideways, along the wing, from root to tip underneath and from tip to root on top.
At slow airspeeds we need a higher AoA, so the difference in pressure between top and bottom of wing is bigger. This means a bigger spanwise (sideways) component of airflow, and when it reaches the wingtips it curls round it more drastically. As the air leaps upwards from the high pressure area to the low pressure area it is sucked inboard towards the greater area of low pressure and down towards the surface of the wing again. As it moves down towards the surface though, it finds the wing has moved on and its inertia means it returns to the high pressure area again. It is again forced sideways and out and up and in and down, and this is the process by which both wake turbulence and induced drag are created. You can also go into the change in effective angle of attack from here, as the downwash is modified by this process and the total reaction is tilted backwards. THIS is the inducing of Induced Drag, and the higher the AoA the more the difference, so the more the tilting, so the more the I.D.
(Pedantic hat on)
Old Dog
You can't sine a vector, only an angle.
Purple Haze
If this doesn't answer your question, email me privately because frankly I feel I can use the practice of explaining without pictures!
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Confident, cocky, lazy, dead.