Sharedfirst_steps / InClass / Inverse Trigonometric Functions.sagewsOpen in CoCalc
%md

We will show you  the inverse trigonometric functions.
* $\sin(x)$: Its inverse is denoted by $\sin^{-1}(x)$ or $\arcsin(x)$.

We will show you the inverse trigonometric functions.

  • sin(x)\sin(x): Its inverse is denoted by sin1(x)\sin^{-1}(x) or arcsin(x)\arcsin(x).
Interact: please open in CoCalc
  • cos(x)\cos(x): Its inverse is denoted by cos1(x)\cos^{-1}(x) or arccos(x)\arccos(x).
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  • tan(x)\tan(x): Its inverse is denoted by tan1(x)\tan^{-1}(x) or arctan(x)\arctan(x). This one probably is the most important one amoung the other inverse trig functions.
@interact(layout=[['size'],['tangent','diagonal','arctangent'],['r']])
def _(tangent=checkbox(label='$tan(x)$'), diagonal=checkbox(default=false,label='$y=x$'), arctangent=checkbox(default=false,label='$tan^{-1}(x)$'),size=10,r=range_slider(-11,11,1,default=(-4,4))):
    t=plot(tan(x),xmin=-pi/2,xmax=pi/2,ymin=-4,ymax=4,legend_label='$tan(x)$')
    diag=plot((x,x),xmin=-4,xmax=4,ymin=-4,ymax=4)
    arct=plot(arctan(x),xmin=r[0],xmax=r[1],ymin=-pi/2,ymax=pi/2,color='red',legend_label='$tan^{-1}(x)$')
    graphs=[]
    if tangent: graphs.append(t)
    if diagonal: graphs.append(diag)
    if arctangent: graphs.append(arct)
    sum(graphs).show(aspect_ratio=1,figsize=size,ticks=pi/4,tick_formatter=pi)
Interact: please open in CoCalc