How do I offset a position with an angle?

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1

I’m not sure how to explain this well so I’ll add a drawing at the end.

Let’s say there is a position 5 feet away from a player. I want to move the position 30 degrees to the left and maintain the 5 feet. How would I do that? (It also would not rotate as the player looks around.)

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2

Someone probably has a more elegant solution but one way to do it is similar to how you rotate a door on its hinge :

local pivot = CFrame.new(0,0,0)
local Distance = 10
local Angle = 30 --- 30°

local Offset =  CFrame.new(0,0,Distance) --- offset away from pivot (un-rotated) 
local Rotation = CFrame.Angles(0, math.rad(Angle),0) ---Rotation using CFrame.Angles
local NewPositoin  =  (pivot  *  Rotation * Offset).Position ---- calculate CFrame then just get the position if you want to

Here it is nicely put into a function:

local function RotatePointAtDist(Point, Angle, Dist)
   local Rotation = CFrame.Angles(0, math.rad(Angle),0)
  return (CFrame.new(Point) *  Rotation * CFrame.new(0,0,Dist)).Position
end

game.Workspace.Part.Position = RotatePointAtDist(Vector3.new(0,0,0),30, 5 )

Did a little research, and if anyone was wondering this is how you can do the pretty much same thing as above but using sin and cos:

local function RotatePointAtDist2( Origin, Angle, Dist)
   local Point = Origin + Vector3.new(0,0,Dist)
   local S, C  = math.sin(math.rad(Angle)), math.cos(math.rad(Angle))
    local X = (Point.x - Origin.X) *  C - (Point.Z - Origin.Z) * S + Origin.X
    local Z = (Point.x - Origin.X) * S + (Point.Z - Origin.Z)*  C + Origin.Z
  return Vector3.new(X, Origin.Y, Z)
end
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