Maple-Worksheet: Trigonometrische Funktionen

Einführung in Maple Übungen

|

|

|

|

Mathematik

Trigonometrische Funktionen

>	restart; with (plots): Warning, the name changecoords has been redefined

sin und cos:

>	plot ([sin(x), cos(x)], x = -2Pi..2Pi, color = [black, red]);

sin und cos

sin und tan:

>	plot ([sin(x), tan(x)], x = -2Pi..2Pi, y = -5..5, color = [black, red], discont = true);

sin und tan

Besondere Werte:

>	sin(Pi/4); cos(Pi/3);

Vereinfachen trigonometrischer Ausdrücke:

>	(sin^2)(x) + (cos^2)(x); simplify (%);

>
simplify (sin(x + Pi/2));
simplify (sin(x)^4 - cos(x)^4);
combine (4*cos(x)^3 - 3*cos(x), trig);

Umformen trigonometrischer Ausdrücke:

>	expand (tan(2x)); expand (sin(3x));

2*tan(x)/(1-tan(x)^2)

Umwandlung vom Bogenmaß ins Winkelmaß:

>	w:= convert (b, degrees); w:= evalf(%); w:= convert (Pi, degrees);

Umwandlung vom Winkelmaß ins Bogenmaß:

>	b:= convert (alphadegrees, radians); b:= convert (30degrees, radians);

Lösen trigonometrischer Gleichungen:

>	solve (sin(x) = cos(x), x);

>	_EnvAllSolutions:= true: lgn:= solve (sin(x) = cos(x), x);

>	alias (k = _Z2): lgn; about (k);

Originally _Z2, renamed _Z2~:
is assumed to be: integer

Arcusfunktionen:

>	simplify (arcsin (sin(x)));

>	assume (x >= -Pi/2, x <= Pi/2); interface (showassumed = 0); simplify (arcsin (sin(x))); simplify (arctan (tan(x)));

x
x

>	plot ([sin(x), arcsin(x)], x = -Pi/2..Pi/2, color = [black, red]);

sin und arcsin

|

|

|

|