HEIDENHAIN TNC 406 - Manual (Page 213)

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) =