# Basic Trigonemetry for Robotic Mechanical Joints

Trigonometry is a branch of mathematic which frequently used in robotics where it’s commonly used in inverse kinematics of mechanical leg / joints, forward kinematics, etc. Trigonometry calculates about angles and sides of a triangle. In trigonemetric, there’s ratios for acute angles:

– sin = opposite  /  hypotenuse

– cos = adjacent / hypotenuse

– tan = opposite  / adjacent

– secant = hypotenuse / adjacent

– cosecant = hypotenuse / opposite

– cotangent = adjacent / opposite

For example here we have a triangle: it’s known that adjacent’s length is 4 and hypotenuse’s length is 5. Based on phytagoras theorem: So :

4²  + b² = 5²

16 + b² = 25

b = √9 = 3

So we got :

Sin R = b / c = 3 / 5, Cos R = a / c = 4 / 5, Tan R = b/a = 3/4, Secant R = c/a = 5/4, Cosecant R = c  / b =5/3, cotangent R = a/b = 4/3

Trigonometry on Equilateral Triangle

For example here, we have an equilateral triangle: Actually that equilateral triangle can be divide into 2 area, something like this : That equilateral triangle when divided into 2 areas, has each 30 degress for it’s top.

Let’s just give name for each angle on cartesius coordinate as x and y: How to calculate sin x, cos x , tan x, sin y, cos y and tan y ?

Have a check on special table of trigonometry : Since sin x is 30 degree = 1/2, where sin = opposite  /  hypotenuse, so sin x = b / c, we figure out that b = 1 and c = 2. To find a based on phytagoras theory:

c² = a² + b²

2² = a² + 1²

4 = a² +  1

a = √3

So cos x = adjacent / hypotenuse  = a / c = √3 / 2

tan x = opposite  / adjacent = b / a = 1/√3

The same goes for sin, cos and tan y.