Analytic representations the symmetric triangle wave with period 2 and varying between -1 and 1 include f(x) | = | 2/π sin^(-1)[sin(π x)] | = | 1 - 2 left bracketing bar 1 - [2(1/2 x + 1/4 (mod 1))] right bracketing bar | = | 1 - 4 left bracketing bar 1/2 - frac(1/2 x + 1/4) right bracketing bar , where frac(x) is the fractional part of x. The triangle wave is implemented in the Wolfram Language as TriangleWave[x].

sawtooth wave | square wave | staircase function | triangle function