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Triangle wave
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=== Expression in trigonometric functions === A triangle wave with period ''p'' and amplitude ''a'' can be expressed in terms of [[sine]] and [[arcsine]] (whose value ranges from β''Ο''/2 to ''Ο''/2): <math display="block">y(x) = \frac{2a}{\pi} \arcsin\left(\sin\left(\frac{2\pi}{p}x\right)\right).</math> The identity <math display="inline">\cos{x} = \sin\left(\frac{p}{4}-x\right)</math> can be used to convert from a triangle "sine" wave to a triangular "cosine" wave. This phase-shifted triangle wave can also be expressed with [[cosine]] and [[arccosine]]: <math display="block">y(x) = a - \frac{2a}{\pi} \arccos\left(\cos\left(\frac{2\pi}{p}x\right)\right).</math>
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