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Trigonometrische Funktionen

> restart; with(plots):
opts:= 'font = [COURIER, 12],
        size = [350, 250]':

sin und cos:

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

trigfkt1 

sin und tan:

> plot([sin(x), tan(x)],
  view = [-2*Pi..2*Pi, -5..5],
  opts,
  color = [black, red],
  discont = true,
  scaling = CONSTRAINED);

sin und tan

Besondere Werte:

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

1/2*2^(1/2)
1/2

Vereinfachen trigonometrischer Ausdrücke:

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

sin(x)^2+cos(x)^2
1

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

cos(x)
1-2*cos(x)^2 
cos(3*x)

Umformen trigonometrischer Ausdrücke:

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

2*tan(x)/(1-tan(x)^2)
4*sin(x)*cos(x)^2-sin(x)

Umwandlung vom Bogenmaß ins Winkelmaß:

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

w := 180*b/Pi*degrees 
w := 57.29577950*b*degrees
w := 180*degrees

Umwandlung vom Winkelmaß ins Bogenmaß:

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

b := 1/180*alpha*Pi
b := 1/6*Pi

Lösen trigonometrischer Gleichungen:

> solve(sin(x) = cos(x), x); 

1/4*Pi

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

lgn := 1/4*Pi+Pi*_Z2

> alias(k = _Z2):
lgn;
about(k); 

1/4*Pi+Pi*k

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

Arcusfunktionen:

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

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, opts,
  color = [black, red]);

trigfkt23