In order for an inverse relation to be a function the invers

In order for an inverse relation to be a function, the inverse must meet the requirements of a function. In Trig (as with some other functions), this can cause a problem. How do we \"get around\" this in Trig so that we can use inverse Trig relationships and still have all of the nice properties we have with functions.

*This is a discussion board assignment so I need to have an answer that thuroghly explains this process in words, not equations. *

Solution

For any function to be Invertible, two things are necessary:

1. It should be One-One - This can be found out by drawing a line parallel to x-axis. It shoult intersect graph at one point only.

2. It shoul be onto - Codomain should be equal to Range.

In trigonometric functions, in order to make a function invertible, we need to restrict its domain (which is the range for inverted function).

Eg : y=Sin x

Its domain is R, But in order to make it invertible, we write y = Arc Sinx where x is between [-1,+1]

By Using such restriction in domains, we can make it invertible and can apply properties!