**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 ➜ 90^{0}

^{ }π radians ➜ 180^{0}^{ }2π radians ➜ 360^{0}

# 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:

Notes:

- Point M coordinates: x = cos(θ), y = sin(θ)
- Equation of the unit cercle: x
^{2}+ y^{2}= 1 - Special case of Pythagora: sin
^{2}(θ) + cos^{2}(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 ?

Solution:

Curve 1: - sin(x)

Curve 2: cos(x-π/4)

Curve 3: 1.5 cos(x/2)

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