HEIDENHAIN TNC 430 - 10.4 Trigonometric Functions; Definitions

HEIDENHAIN TNC 426, TNC 430 361
10.4 Trigonometric Functions
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
n c is the side opposite the right angle
n a is the side opposite the angle a
n b is the third side.
The TNC can find the angle from the tangent:
α = arc tan (a / b) = arc tan (sin α / cos α)
Example:
a = 25 mm
b = 50 mm
α = arc tan (a / b) = arc tan 0.5 = 26.57°
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)=