math.asin() - Lua | Version 5.4 Docs

The math.asin() function in lua returns the inverse sine (in radians) of a number. That is:

∀ x ∊ [-1, 1], math.asin(x) = arcsin(x) = the unique y ∊ [-π/2, π/2] such that sin(y) = x.

Syntax

math.asin(x)

Parameters

x
A number between -1 and 1 (inclusive), representing the sine value of an angle.

Return value

The inverse sine of x, expressed as an angle in radians between -π/2 and π/2 (inclusive). If x is less than -1 or greater than 1, the function returns nil or may trigger an error, as the value is undefined in these cases.

Description

Because math.asin() is a static function, it is always used as math.asin(), rather than as a method of a lua object. This function is commonly used to compute the angle corresponding to a given sine value.

Examples

Using `math.asin()`

print(math.asin(-1))       -- -1.5707963267949 (-π/2)
print(math.asin(0))        -- 0
print(math.asin(0.5))      -- 0.5235987755983 (π/6)
print(math.asin(1))        -- 1.5707963267949 (π/2)

Handling out-of-range values

If the input value is outside the range [-1, 1], the result is undefined, and an error or nil may occur.

-- Correct usage:
print(math.asin(0.75))     -- A valid angle in radians

-- Incorrect usage:
-- print(math.asin(2))      -- Error: argument out of range