Not quite sure where to apply Sin,Cos,Tan and their inverses

So as the name suggests, I have trouble finding where Sin, Cos, and Tan are usable. I have taken trig class and I know the unit circle, the trignometric functions and what they do. I just can’t find where they’d be applicable and how I’d use them in code.


sin, cos can be used with an elapsed time variable to make a part move in a sine/cosine wave pattern (tick() would also work)

Example code: (this will move the part in a circle)

local RunService = game:GetService("RunService")
local Sine = 0

local Part = script.Parent
local PartCFrame = Part.CFrame

RunService.Heartbeat:Connect(function(DeltaTime: number)
	Sine += DeltaTime
	Part.CFrame = PartCFrame * * 5, 0, math.cos(Sine) * 5)

So *5 really just amplifies the movement, it has no other use, correct?

math.sin() returns a value between -1 and 1, so therefore multiplication by 5 just makes it move by 5 studs. I can also think of an example with the Rotation property of GUIs, you can use it to smoothly make it turn left to right.

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Is there a specific reason why math.sin() comes before math.cos() in the new cframe?

Late reply, but ill gave a few:

Moving objects in a wave pattern is one of them for sine/cosine:

local amplitude = 5
local frequency = 2 * math.pi / 60 

for i = 1, 360 do
    local y = amplitude * math.sin(frequency * i)
    object.Position =, y, object.Position.Z)

For tangent, you can calculate the horizontal field of view of a camera:

function calculateHorizontalFOV(verticalFOV, aspectRatio)
     local verticalFOVInRadians = math.rad(verticalFOV)
     local tanOfHalfVerticalFOV = math.tan(verticalFOVInRadians / 2)
     local tanOfHalfHorizontalFOV = tanOfHalfVerticalFOV * aspectRatio
     local horizontalFOV = 2 * math.deg(math.atan(tanOfHalfHorizontalFOV))
     return horizontalFOV

local verticalFOV = 60
local aspectRatio = 16/9
local horizontalFOV = calculateHorizontalFOV(verticalFOV, aspectRatio)

Using the inverse tangent can help find the angle between two points:

function calculateAngle(x1, y1, x2, y2)
      local deltaY = y2 - y1
      local deltaX = x2 - x1
      local angle = math.atan(deltaY / deltaX)
      local angleInDegrees = math.deg(angle)
      return angleInDegrees

local x1, y1 = 1, 2
local x2, y2 = 4, 6
local angle = calculateAngle(x1, y1, x2, y2)
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