Inverse Trigonometry Fundamental Concept

 Some basic concepts of Inverse Trigonometry:

1). To map real numbers back to angles.

2). An inverse of the sine function is denoted by arc sin(x).

Domain: [-1,1]

Range:  [-π/2, π/2]

It is also called the principal branch range.

4). The graph of arc sin(x) is obtained from sin(x) by interchanging x and y-axes.

5). Graph of the arc sin(x) is the mirror image of sin(x) with the axis of symmetry is y=x.

6). Inverse of cos(x) is denoted by arc cos(x).

Domain:  [-1,1]

Range : [0,π]

It is also called principal branch range.

7). arc tan(x)

Domain : Real Number

Range: (-π/2, π/2)

It is also principal branch range.

8).  arc sec(x)

Domain: R -(-1, 1)

Range: [0, π] -{ π/2}

9).arc cosec(x)

Domain : R -(-1, 1)

Range: [-π/2, π/2]-{0}

10). arc cot(x)

Domain: R

Range: (0, π)

Here R denotes real number and range mentioned is principal branch range.