Sections:

Graphing Trigonometric Functions, Page 15

Principal Values (continued)

The graphs of these specific functions with principal values are just portions of the graphs you created for the sine, cosine, and tangent functions. The domain of these functions is listed in their definitions. 

Like sine, cosine, and tangent, these functions (Sine, Cosine, and Tangent) also have inverses.
y = Sin(x) has an inverse y = Sin-1 or y = Arc sin(x).
y = Cos(x) has an inverse y = Cos-1 or y = Arc cos(x).
y = Tan(x) has an inverse y = Tan-1 or y = Arc tan(x).

The following is a summary of these functions, including their domain and range: 

                           Function
 

Domain

Range

y = Sin(x)

-pi/2 is less than or equal to x is less than or equal to pi/2

-1 is less than or equal to y is less than or equal to 1

y = Arc sin(x)

-1 is less than or equal to x is less than or equal to 1

-pi/2 is less than or equal to y is less than or equal to pi/2

y = Cos(x)

zer is less than or equal to x is less than or equal to pi

-1 is less than or equal to y is less than or equal to 1

y = Arc cos(x)

-1 is less than or equal to x is less than or equal to 1

zero is less than or equal to y is less than or equal to pi

y = Tan(x)

-pi/2 is less than x is less than pi/2

All Real Numbers

y = Arc tan(x)

All Real Numbers

-pi/2 is less than y is less than pi/2