Periodic Identities
by EngliSea on 2026-11-06


Periodic Identities

SOH CAH TOA
sin(x+2nπ) = sin(x)
cos(x+2nπ) = cos(x)
tan(x+nπ) = tan(x)
csc(x+2nπ) = csc(x)
sec(x+2nπ) = sec(x)
cot(x+nπ) = cot(x)

Slope is rise over run and 1 turn is 2π radians.
⦶(x+n) = ⦶(x)
⊖(x+n) = ⊖(x)
⊘(x+n/2) = ⊘(x)
⦶⁻¹(x+n) = ⦶⁻¹(x)
⊖⁻¹(x+n) = ⊖⁻¹(x)
⊘⁻¹(x+n/2) = ⊘⁻¹(x)


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Periodic Identities.

Soh Caa Toa.
Sine of, x+2nπ equals sine of x.
Cosine of, x+2nπ equals cosine of x.
Tangent of, x+nπ equals tangent of x.
Co-secant of, x+2nπ equals co-secant of x.
Secant of, x+2nπ equals secant of x.
Co-tangent of, x+nπ equals co-tangent of x.

Slope is rise over run and 1 turn is 2π radians.
Rise of, x+n equals rise of x.
Run of, x+n equals run of x.
Slope of, x+n/2 equals slope of x.
Rise reciprocal of, x+n equals rise reciprocal of x.
Run reciprocal of, x+n equals run reciprocal of x.
Slope reciprocal of, x+n/2 equals slope reciprocal of x.


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