HEIDENHAIN TNC 407 (280 580) User Manual - Manual (Page 193)

TNC 425/TNC 415 B/TNC 407 7-8
7 Programming with Q Parameters
Fig. 7.3: Sides and angles on a right triangle
Soft key
b
c
a
α
7.3 Trigonometric Functions
Sine, cosine and tangent are terms for the ratios of the sides of right
triangles. The TNC can save you a lot of time spent searching in hand-
books of trigonometric functions by calculating these functions for you.
For a right triangle:
Sine: sin
α
= a / c
Cosine: cos
α
= b / c
Tangent: tan
α
= a / b = sin
α
/ cos
α
Where:
• c is the side opposite the right angle
• a is the side opposite the angle
α
• b the third side
The angle can be found from the tangent:
α
= arctan
α
= arc tan (a / b) = arc tan (sin
α
/ cos
α
)
Example: a = 10 mm
b = 10 mm
α
= arc tan (a / b) = arc tan 1 = 45°
furthermore: a 2 + b 2 = c 2 (a 2 = a . a)
c =
√
a 2 + b 2
Press the “trigonometric functions” soft key to call the following options:
Overview
FN6: SINE
e.g. FN6: Q20 = SIN–Q5
Calculate sine of an angle in degrees (°) and
assign it to a parameter
FN7: COSINE
e.g. FN7: Q21 = COS–Q5
Calculate cosine of an angle in degrees (°) and
assign it to a parameter
FN8: ROOT-SUM OF SQUARES
e.g. FN8: Q10 = +5 LEN +4
Take the square root of the sum of two
squares and assign it to a parameter
FN13: ANGLE
e.g. FN13: Q20 = +10 ANG–Q1
Calculate the angle from the arc tangent of two
sides or from the sine and cosine of the angle
(0°
−
angle
−
360°) and assign it to a parameter