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.

• $\sin(x)$: Its inverse is denoted by $\sin^{-1}(x)$ or $\arcsin(x)$.
• $\cos(x)$: Its inverse is denoted by $\cos^{-1}(x)$ or $\arccos(x)$.
• $\tan(x)$: Its inverse is denoted by $\tan^{-1}(x)$ or $\arctan(x)$. 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)