Trigonometry Primer

1.    Introduction

Trigonometry is everywhere and used in many branches of science and technology: geography, astronomy, electrical engineering, architecture, etc…

The basic concepts are presented here, mostly in pictures and a few formulas.  Also, there is a short test at the end !

2.    Unit of measure of angles

Two types of units are used for angles: radians and degrees. This is important to master fully and be able to easily go from one set of units to the other.

Angle θ in radians = length of the arc intercepted by the angle θ on the unit circle.

θ = 2π that corresponds to one full rotation on the unit circle, is the perimeter of the unit circle of radius of 1 (Perimeter = 2 π * Radius).

  • π/2 radians  ➜  900
  • π radians      ➜ 1800
  • 2π radians    ➜ 3600

3.    Sinus and cosinus formulas

 Considering the rectangle triangle below:

Sinus, cosinus and tangent formulas:

  • Sin(θ) =  O / H      = Opposite / Hypotenuse
  • Cos(θ) = A / H       = Adjacent / Hypotenuse
  • Tg(θ) =   O / A       = Opposite / Adjacent

Helpful mnemonic: SOH-CAH-TOA

4.    Trigonometric circle

 The trigonometric circle is an important tool to work with angles, for a clear understanding of the relationship to the trigonometric functions and periodicity:



  • Point M coordinates: x = cos(θ), y = sin(θ)
  • Equation of the unit cercle: x2 + y2 = 1
  • Special case of Pythagora: sin2(θ) + cos2(θ) = 1

5.    Trigonometric circle and Sinus function

How the trigonometric circle relates to the Sinus function graph:


There is a similar figure for cosinus; compared to the sinus curve, cosinus is shifted by π/2 to the left.

6.    Test yourself

Can you identify the following trigonometric functions curves ?




Curve 1: - sin(x)

Curve 2: cos(x-π/4)

Curve 3: 1.5 cos(x/2)