7.6: The Inverse of Trigonometric Functions

Recall from Chapter 3.8 the definition of an inverse function:


Let f be a one-to-one function with domain D and range R. A function g with domain R and range D is the inverse function of f.



In Chapter 7.6, we will take the inverse of trigonometric functions sine, cosine, and tangent. These are denoted several ways:


Sine:




Cosine:
 

Tangent:






 Because you can only take the inverse of a one-to-one function, we must restrict the domain of the trigonometric functions, since they are not one-to-one.

Sine

Cosine

Tangent

Although we alter the domains, the ranges remain the same.

Sine: -1 ≤ x ≤ 1

Cosine: -1 ≤ x ≤ 1

Tangent: -∞ < x < ∞

Properties of the inverse sine:

 

       if 

       if 

Properties of the inverse cosine:

      if 

      if

Properties of the inverse tangent:

      if 

   

      if 

- Olivia Darany