beautypg.com

4 trigonometric functions, Definitions – HEIDENHAIN TNC 406 User Manual

Page 213

background image

192

10 Programming: Q Parameters

1

0.4 T

rig

onometr

ic F

u

nctions

10.4 Trigonometric Functions

Definitions

Sine, cosine and tangent are terms designating the ratios of sides of
right triangles. For a right triangle, the trigonometric functions of the
angle a are defined by the following equations:

where

„

c is the side opposite the right angle

„

a is the side opposite the angle a

„

b is the third side.

The TNC can find the angle from the tangent:

α

= arctan (a / b) = arctan (sin

α

/ cos

α

)

Example:

a = 10 mm

b = 10 mm

α

= arctan (a / b) = arctan 1 = 45°

Furthermore:

a² + b² = c² (where a² = a x a)

Sine:

sin

α

= a / c

Cosine:

cos

α

= b / c

Tangent:

tan

α

= a / b = sin

α

/ cos

α

b

c

a

α

c

(a² + b²)

=

This manual is related to the following products: