HEIDENHAIN TNC 426, User Manual

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HEIDENHAIN TNC 426, TNC 430 361
1
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:
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) =