Question

draw the graph of sin inverse x using the graph of sin x demonstrate the concept of mirror reflection (about the line y = x)​

Answer 1

1) Graph of

is symmetric about the line y=x

2) Graph of  

is not symmetric about the line y=x.

We know that sin x is periodic function with time period 2π.So sin function can not be invertible in its complete domain.

If a function is bijective than only it can be invertible.

So,to defined

we have to first adjust the domain of the sin function,in which it can be one-one and onto(i.e. Bijective)

So,[-π/2,π/2] is the suitable part,which is near to origin.

Now,

has domain [-π/2,π/2] and range [-1,1],because range and domain are interchanged while a function is being inverse.

Hence the graph of

is shifted to Y-axis.(graph1)

Graph 2 is graph of sin x.

Graph 3 is both sin and sin inverse functions.

Graph 4 shown symmetry along line y= x.

By the same way graph of cos inverse can be drawn as shown in graph 5