Actually you can do mecanum without trig. Just like the arcade drive is figuring out how to sum up the motor in the right way based on the joystick input. It certainly isn't an overly efficient mecanum drive as scaling is an issue, but you can get the idea of it. I think its actually a good problem solving task to do the mecanum without trig
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Actually doing an encoder based mecanum drive could be done without trig too. Its only when you start going field centric that you really need trig.
Also the trig isn't too bad either, you could find it online. Just treat the left joystick as a circle and find the angle and distance from center based on the 2 values.
x^2 + y^2 = magnitude^2
angle = arctan(y/x)
soh cah toa
sin = opposite over hypotenuse
cos = adjacent over hypotenuse
tan = opposite over adjacent
cos(angle)*mag = y mag
sin(angle)*mag = x mag
give all 4 motor the y mag
top right back left y mag + x mag
top left back right y mag - x mag
i may have the side flipped not sure
programming a mec via trig is a lot easier than doing it without it, that why i suggest you try doing it by taking all joystick values / 2 and setting the motors via that. its def possible. for scaling reasons i'd leave out rotation at first.
if your feeling really ambitious let a gyro set the rotation value and you just set the x and y.