|
Appendix III. Guide on formulas |
Scroll |
The guide contains the following formulas:
•identity transformations:
•Short multiplication formulas,
•trigonometrical formulas:
•Addition of trigonometrical functions,
•Product of trigonometrical functions,
In column Equation, the standard view of formulas is presented, and in column Syntax KOMPAS-3D — their representation in the syntax of KOMPAS-3D. The text from the column Syntax KOMPAS-3D can be copied via the clipboard into the cells of the Variables panel and the fields of the Parameters panel, for example, when specifying the parameters of a curve by law.
Formula |
Syntax KOMPAS-3D |
|||
|
a/b |
= |
(a*m)/(b*m) |
|
|
a/b |
= |
(a/m)/(b/m) |
|
|
(a/b)/(c/d) |
= |
a/b*d/c |
|
= |
(a*d)/(b*c) |
|||
|
a/b*c/d |
= |
(a*c)/(b*d) |
|
|
a/b+c/d |
= |
(a*d+b*c)/(b*d) |
|
a/b-c/d |
= |
(a*d-b*c)/(b*d) |
||
|
c/((n+a)*(n+b)) |
= |
(1/(n+a)-1/(n+b))*c/(b-a) |
|
Formula |
Syntax KOMPAS-3D |
|||
|
a^2-b^2 |
= |
(a-b)*(a+b) |
|
|
(a+b)^2 |
= |
a^2+2*a*b+b^2 |
|
|
(a-b)^2 |
= |
a^2-2*a*b+b^2 |
|
|
a^3+b^3 |
= |
(a+b)*(a^2-a*b+b^2) |
|
|
a^3-b^3 |
= |
(a-b)*(a^2+a*b+b^2) |
|
|
(a+b)^3 |
= |
a^3+3*a^2*b+3*a*b^2+b^3 |
|
|
(a-b)^3 |
= |
a^3-3*a^2*b+3*a*b^2-b^3 |
|
Formula |
Syntax KOMPAS-3D |
|||
|
sin(a+b) |
= |
sin(a)*cos(b) + cos(a)*sin(b) |
|
|
sin(a-b) |
= |
sin(a)*cos(b)-cos(a)*sin(b) |
|
|
cos(a+b) |
= |
cos(a)*cos(b)-sin(a)*sin(b) |
|
|
cos(a-b) |
= |
cos(a)*cos(b)+sin(a)*sin(b) |
|
|
tan(a+b) |
= |
(tan(a)+tan(b))/(1-tan(a)*tan(b)) |
|
|
tan(a-b) |
= |
(tan(a)-tan(b))/(1+tan(a)*tan(b)) |
|
Formula |
Syntax KOMPAS-3D |
|||
|
sin(2*a) |
= |
2*sin(a)*cos(a) |
|
|
sin(2*a) |
= |
(2*tan(a))/(1+tan(a)^2) |
|
|
cos(2*a) |
= |
cos(a)^2-sin(a)^2 |
|
|
cos(2*a) |
= |
2*cos(a)^2-1 |
|
|
cos(2*a) |
= |
1-2*sin(a)^2 |
|
|
tan(2*a) |
= |
(2*tan(a))/(1-tan(a)^2) |
|
|
sin(3*a) |
= |
3*sin(a)-4*sin(a)^3 |
|
|
cos(3*a |
= |
4*cos(a)^3-3*cos(a) |
|
|
tan(3*a |
= |
(3*tan(a)-tan(a)^3)/(1-3*tan(a)^2) |
|
Addition of trigonometrical functions
Formula |
Syntax KOMPAS-3D |
|||
|
sin(a)+sin(b) |
= |
2*sin((a+b)/2)*cos((a-b)/2) |
|
|
sin(a)-sin(b) |
= |
2*sin((a-b)/2)*cos((a+b)/2) |
|
|
cos(a)+cos(b) |
= |
2*cos((a+b)/2)*cos((a-b)/2) |
|
|
cos(a)-cos(b) |
= |
-2*sin((a+b)/2)*sin((a-b)/2) |
|
|
tan(a)+tan(b) |
= |
sin(a+b)/(cos(a)*cos(b)) |
|
|
tan(a)-tan(b) |
= |
sin(a-b)/(cos(a)*cos(b)) |
|
Product of trigonometrical functions
Formula |
Syntax KOMPAS-3D |
|||
|
sin(a)*sin(b) |
= |
1/2*(cos(a-b)-cos(a+b)) |
|
|
cos(a)*cos(b) |
= |
1/2*(cos(a-b)+cos(a+b)) |
|
|
sin(a)*cos(b) |
= |
1/2*(sin(a-b)+sin(a+b)) |
|
Formula |
Syntax KOMPAS-3D |
|||
|
cos(a)^2 |
= |
(1+cos(2*a))/2 |
|
|
sin(a)^2 |
= |
(1-cos(2*a)/2 |
|
|
cos(a)^3 |
= |
(3*cos(a)+cos(3*a))/4 |
|
|
sin(a)^3 |
= |
(3*sin(a)-sin(3*a))/4 |
|
Formula |
Syntax KOMPAS-3D |
|||
|
2*R |
= |
L1/sin(a) |
|
= |
L2/sin(b) |
|||
= |
L3/sin(c) |
|||
|
L3^2 |
= |
L1^2+L2^2-2*L1*L2*cos(c) |
|
|
(L1-L2)/(L1+L2) |
= |
tan((a-b)/2)/tan((a+b)/2) |
|
|
R |
= |
p/(4*cos(a/2)*cos(b/2)*cos(c/2)) |
|
|
r |
= |
4*R*sin(a/2)*sin(b/2)*sin(c/2) |
|
|
S |
= |
1/2*L1*L2*sin(c) |
|
|
S |
= |
2*R^2*sin(a)*sin(b)*sin(c) |
|
