What do you want to achieve? Keep it simple and clear!

Understand Trigonometry in script.

What is the issue? Include screenshots / videos if possible!

This script makes the characters head rotate relative to your cameras position. But I do not get how the trigonometry works.

I get that arcsine of opposite/hypotenuse = degrees, but why is the opposite site of the triangle the x and then the y coordinate of the cameras lookvector? From what I understand you make a vector from the humanoidrootpart to the camera and then get the cameras lookvector but I dont understand what happens after this (see picture). Thanks for the Help!

local camera = workspace.CurrentCamera
local character = game.Players.LocalPlayer.Character
local root = character:WaitForChild("HumanoidRootPart")
local neck = character:FindFirstChild("Neck", true)
local yOffset = neck.C0.Y
local CFNew, CFAng, asin = CFrame.new, CFrame.Angles, math.asin
game:GetService("RunService").RenderStepped:Connect(function()
local cameraDirection = root.CFrame:toObjectSpace(camera.CFrame).lookVector
if neck then
neck.C0 = CFNew(0 , yOffset, 0) * CFAng(0, -asin(cameraDirection.x), 0) * CFAng(asin(cameraDirection.y), 0, 0)
end
end)

What solutions have you tried so far? Did you look for solutions on the Developer Hub?

Tried looking at the devforum for trigonometry in 3d space.

Technically the trig in the code in question is slightly wrong for the yaw (Y axis) rotation.

The hypotenuse of the triangle @dthecoolest drew is not “the LookVector”, but rather “the LookVector when it’s y component is 0”, which probably does not have a length of 1.

So to use sine like that you’d need to do

local x, y, z = cameraDirection.X, cameraDirection.Y, cameraDirection.Z
local hyp = math.sqrt(x*x + z*z)
local yaw = math.asin(x / hyp)

Or just use arctangent instead:

math.atan2(-x, z)

The pitch one (math.asin(y)) is correct because the hypotenuse is actually the look vector, while the “opposite” side is indeed cameraDirection.Y

For @SejeBlomst and others it is important to take note that a lot of trigonometry is approximated especially for procedural animations as accuracy and proper maths isn’t the goal.

It’s purely for animation purposes.

Another example of improper trig below

If you want to see accurate angle measurements I recommend looking at turret scripts like this one made by @ThanksRoBama which uses atan2 as @nicemike40 has mentioned for both the pitch and yaw axis.

These scripts are the ones that need to be precise and use proper trigonometry to achieve the accurate effect of pointing to the target.