# Trigonometry

The word trigonometry is derived from the Greek words tri = three, gon = sides and metron = measure.

• sin θ = A/H
• cos θ = O/H
• tan θ = A/O
• cosec θ = H/A
• sec θ = H/O
• cot θ = O/A
Reciprocal Identities
sin θ =
$\frac{1}{\mathrm{csc \theta }}$
csc θ =
$\frac{1}{\mathrm{sin \theta }}$
cos θ =
$\frac{1}{\mathrm{sec \theta }}$
sec θ =
$\frac{1}{\mathrm{cos \theta }}$
tan θ =
$\frac{1}{\mathrm{cot \theta }}$
cot θ =
$\frac{1}{\mathrm{tan \theta }}$
Quotient Identities
tan θ =
$\frac{\mathrm{sin \theta }}{\mathrm{cos \theta }}$
cot θ =
$\frac{\mathrm{cos \theta }}{\mathrm{sin \theta }}$
Pythagorean Identities
Sin2θ + Cos2θ = 1
Sec2θ - Tan2θ = 1
Cosec2θ - Cot2θ = 1

### Trigonometry Ratios:

Degrees 00 300 450 600 900 1800 2700 3600
Radions 0 π/6 π/4 π/3 π/2 π 3π/2
Sin θ 0 1/2 $1}{\sqrt{2}}$ $\sqrt{3}}{2}$ 1 0 -1 0
Cos θ 1 $\sqrt{3}}{2}$ $1}{\sqrt{2}}$ 1/2 0 -1 0 1
Tan θ 0 $1}{\sqrt{3}}$ 1 $\sqrt{3}$ 0 0
Cot θ $\sqrt{3}$ 1 $1}{\sqrt{3}}$ 0 0
Sec θ 1 $2}{\sqrt{3}}$ $\sqrt{2}$ 2 -1 1
Cosec θ 2 $\sqrt{2}$ $2}{\sqrt{3}}$ 1 -1