math.atan

local result = math.atan(
    vertical,
    horizontal = 1
)

Type	Name	Description
`number`	vertical	Vertical component (or the sole value when horizontal is omitted)
`number`	horizontal	Horizontal component - used for two-argument atan2 behavior

Type	Name	Description
`number`	result	Arc tangent of vertical/horizontal in radians, in the range [-pi, pi]

Arc tangent of 1 is pi/4

local result = math.atan(1)

engine.print("info", result) -- 0.78539816339745

Arc tangent of 0 is 0

local result = math.atan(0)

engine.print("info", result) -- 0.0

Two-argument atan for a 45 degree angle

local result = math.deg(math.atan(1, 1))

engine.print("info", result) -- 45.0

Angle pointing left along the negative x axis

local result = math.deg(math.atan(0, -1))

engine.print("info", result) -- 180.0

Compute heading angle from a direction vector

local dir_x, dir_y = 3, -3
local angle_deg = math.deg(math.atan(dir_y, dir_x))

engine.print("info", angle_deg) -- -45.0

Get angle from one point to another

local x1, y1 = 0, 0
local x2, y2 = 5, 5
local angle_deg = math.deg(math.atan(y2 - y1, x2 - x1))

engine.print("info", angle_deg) -- 45.0

Verify atan and tan are inverses in range

local angle = math.pi / 4
local result = math.atan(math.tan(angle))

engine.print("info", result) -- 0.78539816339745