HEIDENHAIN TNC 426B (280 472) ISO programming - Manual (Page 273)

10 Programming: Q Parameters 258
10.4 Trigonometric Functions
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:
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 (hypotenuse)
■ a is the side opposite the angle (opposite)
■ b is the third side (adjacent)
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:
a 2 + b 2 = c 2 (where a 2 = a x a)
c = √ (a 2 + b 2 )
Programming trigonometric functions
Press the TRIGONOMETRY soft key to call the trigonometric
functions. The TNC then displays the soft keys that are listed in the
table at right.
Programming: compare „Example: Programming
fundamental operations“.
b
c
a
α
Function Soft key
D06: SINE
Example D06 Q20 P01 –Q5 *
Calculate the sine of an angle in
degrees (°)
and assign it to a parameter.
D07: COSINE
Example D07 Q21 P01 –Q5 *
Calculate the cosine of an angle in
degrees (°) and assign it to a parameter.
D08: ROOT-SUM OF SQUARES
Example D08 Q10 P01 +5 P02 +4 *
Calculate and assign length from two values
D13: ANGLE
Example D13 Q20 P01 +10 P02 –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.
1
0.4
T
ri
g
onometr
ic F
unctions
Mkap10.pm6 29.06.2006, 08:06 258