HEIDENHAIN TNC 410 ISO Programming - Manual (Page 362)

336 10 Programming: Q Parameters
1
0
.4 T
rig
ono
metr
ic F
u
nction
s
10.4 Trigonometric Functions
Definitions
Sine, cosine and tangent are terms designating the ratios of sides of
right triangles. In this case:
where
n c is the side opposite the right angle
n a is the side opposite the angle
α
n b is the third side.
The TNC can find the angle from the tangent
α
= arctan
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) =