Question

Draw the graph of y = sin -¹x (or any other inverse
trigonometric function), using the graph of
y = sin x (or any other relevant trigonometric
function). Demonstrate the concept of mirror line
(about y = x) and find its domain and range. ​

Answer 1

The domain and range for any equation can be defined as -

If y = f(x),

The possible attainable values of y is called Range.

The possible values of variable x with respect to the function is called Domain.

For the given question, we can write -

y = sin(x) ———- (1)

Sin(x) always lies between -1 to +1.

It means in eqn(1), value of y will lie between -1 to +1.

Hence, Range is (-1,+1)

Also, sin function is defined for all real numbers ranging from (-Inf) to (+Inf).

It means, all real numbers can be put in the place of x, given in eqn(1).

Hence, Domain is (-∞,+∞).