3509-Funções trigonométricas.sagews

Funções trigonométricas

SIN=plot(sin(x),(-2*pi,2*pi),aspect_ratio=1,color='red')

SIN.show()

COS=plot(cos(x),(-2*pi,2*pi),aspect_ratio=1,color='green')

COS.show()

show(SIN+COS)

TAN=plot(tan(x),(-2*pi,2*pi),aspect_ratio=1,color='blue', ymin=-10, ymax=10)
COT=plot(cot(x),(-2*pi,2*pi),aspect_ratio=1,color='orange', ymin=-10, ymax=10)

TAN.show()

COT.show()

show(TAN+COT)

ARCSIN=plot(arcsin(x),(-1,1),ymin=-2, ymax=2,aspect_ratio=1,color='red')

ARCSIN

ARCCOS=plot(arccos(x),(-1,1),ymin=-2, ymax=4,aspect_ratio=1,color='blue')

ARCCOS.plot()

plot(ARCSIN+ARCCOS, aspect_ratio=1)

var('y')
ArcS=arcsin(y)

ArcS.diff(y)

1/sqrt(-y^2 + 1)

ArcC=arccos(y)

ArcC.diff(y)

-1/sqrt(-y^2 + 1)

ARCTG=plot(arctan(x),(-5,5),aspect_ratio=1, color='blue')
ARCCTG=plot(arccot(x),(-5,5),aspect_ratio=1, color='brown')

diff(arctan(x))

1/(x^2 + 1)

diff(arccot(x))

-1/(x^2 + 1)

show(ARCTG+ARCCTG)

Funções trigonométricas hiperbólicas

SINH=plot(sinh(x),(-3,3),aspect_ratio=1,color='blue')
COSH=plot(cosh(x),(-3,3),aspect_ratio=1,color='red')

show(SINH+COSH)

diff(sinh(x))

cosh(x)

diff(cosh(x))

sinh(x)

TH=plot(tanh(x),(-2,2),aspect_ratio=1,color='green')

show(TH)

plot(coth(x),ymin=-6,ymax=6)

diff(tanh(x))

-tanh(x)^2 + 1

diff(coth(x))

-csch(x)^2

diff(arctanh(x))

-1/(x^2 - 1)

diff(arccoth(x))

-1/(x^2 - 1)

plot(arctanh(x),xmin=-1,xmax=1)

P1=plot(arccoth(x),(-3,-1),color='red')
P2=plot(arccoth(x),(1,2),color='red')

show(P1+P2)