Sine Approximation

How to implement a sine approximation in HTSL using Bhāskara I's sine approximation formula.

1 min read
Last Updated on November 2, 2025
0 views

This sine approximation uses Bhāskara I’s sine approximation:

sinx4x(180x)40500x(180x)\sin x^\circ \approx \frac{4 \, x \, (180 - x)}{40500 - x \, (180 - x)}

This approximation works well for practical purposes in Housing because it uses degrees and is accurate to within about 0.0016 of the actual sine value for angles between 0° and 180°. The maximum relative error is less than 1.8%.

It can be implemented in just seven actions.

sin.htsl

var output = %var.player/input%
var output -= 180D
var output *= %var.player/input%
var temp += %var.player/output%
var temp = 40500D
var output *= -4D
var output /= %var.player/temp%