Tangent and Reciprocal Identities
by EngliSea on 2026-11-05


Tangent Identities

SOH CAH TOA
tan(x) = sin(x)/cos(x)
cot(x) = cos(x)/sin(x)

Slope is rise over run.
⊘(x) = ⦶(x)/⊖(x)︱⊘⁻¹(x) = ⊖(x)/⦶(x)

Reciprocal Identities

SOH CAH TOA
csc(x) = 1/sin(x)
sec(x) = 1/cos(x)
cot(x) = 1/tan(x)

Slope is rise over run.
⦶⁻¹(x) = 1/⦶(x)︱⊖⁻¹(x) = 1/⊖(x)︱⊘⁻¹(x) = 1/⊘(x)

_
Tangent Identities.
Soh Caa Toa.
tangent of x equals sine of x over cosine of x.
cotangent of x equals cosine of x over sine of x.
Slope is rise over run.
slope of x equals rise of x over run of x.
slope reciprocal of x equals run of x over rise of x.

Reciprocal Identities.
Soh Caa Toa.
Co-secant of x equals 1 over sine of x.
Secant of x equals 1 over cosine of x.
Co-tangent of x equals 1 over tangent of x.
Slope is rise over run.
Rise reciprocal of x equals 1 over rise of x.
Run reciprocal of x equals 1 over run of x.
Slope reciprocal of x equals 1 over slope of x.