HEIDENHAIN iTNC 530 (340 420) - Manual (Page 409)

HEIDENHAIN iTNC 530 381
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0
.4 T
rig
onometr
ic F
unctions
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
a = arctan (a / b) = arctan (sin a / cos a)
Example:
a = 25 mm
b = 50 mm
a = arctan (a / b) = arctan 0.5 = 26.57°
Furthermore:
a² + b² = c² (where a² = a x a)
Sine: sin a = a / c
Cosine: cos a = b / c
Tangent: tan a = a / b = sin a / cos a
b
c
a
α
c (a² + b²) =