Name        

Notation        

Ratio

Period

Asymptotes

Sine

sin(θ)

$\frac{\mathrm{opposite}}{\mathrm{hypotenuse}}$

2π or 360 degrees

none

Cosine

cos(θ)

$\frac{\mathrm{adjacent}}{\mathrm{hypotenuse}}$

2π or 360 degrees

none

Tangent

tan(θ)

$\frac{\mathrm{opposite}}{\mathrm{adjacent}}$

π or 180 degrees

 $\frac{\mathrm{\π}}{2}\+k\cdot \mathrm{\π}\,$ where k is an integer

Cosecant

csc(θ)

$\frac{\mathrm{hypotenuse}}{\mathrm{opposite}}$

2π or 360 degrees

$k\cdot \mathrm{\π}\,$ where k is an integer$$

Secant

sec(θ)

$\frac{\mathrm{hypotenuse}}{\mathrm{adjacent}}$

2π or 360 degrees

$\frac{\mathrm{\π}}{2}\+k\cdot \mathrm{\π}\,$ where k is an integer$$

Cotangent

cot(θ)

$\frac{\mathrm{adjacent}}{\mathrm{opposite}}$

π or 180 degrees

$k\cdot \mathrm{\π}\,$ where k is an integer$$