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There are such formulas on the internet you can find. The calculator doesn't have sin, cos, and tan, though there are some chips people have made that let you use those functions.

I would probably do it a different way, though. It's a little complicated conceptually, but should work perfectly. Create a block with a tag grouped with it--central but moved further away in one direction. This will be your readout. Wire its scene transform into a chip outside of that group. You can split it (add a splitter, wire the scene transform into it) to get just the position if you like.

Now, outside that group make an emitter, and link it to that cube group. In the last tab, turn on "emit wires" so that the logic stays intact. You probably want it in "once" mode so it just emits a single instance.

Now, we need to make a scene transform so we can set where the object will be emitted and its rotation. To do that, add a combiner, and set it to "scene transform" mode. Wire the value you want for (x1, y1, z1) into the position input. Wire the rotation you want into the rotation input (if you don't have a rotation fat wire, you can make one with another combiner).

Now, when you turn on the emitter, it will spit out that cube at the correct position and rotation, and the tag will give you the position of that rotated point.

I know that all sounds a bit complicated, but it's probably actually cheaper than the sin/cos/tan chips. So up to you.