## Tuesday, November 27, 2007

### Graphs of inverse trigonometric

Graphs of Inverse Trigonometric Functions

The inverse Sine graph below shows the values of the inverse sine function in a range of 0 to 2π, for values of X between -1 or +1. The inverse function is not defined for X larger than 1 and less than -1. That is because the Sine of any angle is between +1 and -1.

You can see that for a given value of X, there are two values of the angle that fit. For example, when X = 0.2, and a line vertical to the X axis is drawn through that point, there would be two points of intersection at 11.5° and 168.5°. These points in radians, would correspond to the points shown on the graph which are 0.201 and 2.941.

The graph of the inverse cosine function below shows the inverse cosine function in a range of 0 to 2π, for the values of X between +1 and -1 because the cosine of any angle cannot be larger than +1 or less than -1. Just like the inverse sine function, there are two values of the angle that fit. When X = 0.2, and a vertical line is drawn through this point, there would be two intersection points at 78.5° and 281.5°. In radians, these points would be 1.370 and 4.911 shown on the graph.

The graph of the inverse tangent function below shows the values of the inverse tangent function in a range of 0 to 2π. The inverse function is defined for all values of X. There are two values of the angle that fit just like the inverse sine and cosine functions. When X = 0.2, and a vertical line is drawn through this point, the two points of intersection would be 11.3° and 191.3°. In radians, they would be 0.197 and 3.339.

The inverse Sine graph below shows the values of the inverse sine function in a range of 0 to 2π, for values of X between -1 or +1. The inverse function is not defined for X larger than 1 and less than -1. That is because the Sine of any angle is between +1 and -1.

You can see that for a given value of X, there are two values of the angle that fit. For example, when X = 0.2, and a line vertical to the X axis is drawn through that point, there would be two points of intersection at 11.5° and 168.5°. These points in radians, would correspond to the points shown on the graph which are 0.201 and 2.941.

The graph of the inverse cosine function below shows the inverse cosine function in a range of 0 to 2π, for the values of X between +1 and -1 because the cosine of any angle cannot be larger than +1 or less than -1. Just like the inverse sine function, there are two values of the angle that fit. When X = 0.2, and a vertical line is drawn through this point, there would be two intersection points at 78.5° and 281.5°. In radians, these points would be 1.370 and 4.911 shown on the graph.

The graph of the inverse tangent function below shows the values of the inverse tangent function in a range of 0 to 2π. The inverse function is defined for all values of X. There are two values of the angle that fit just like the inverse sine and cosine functions. When X = 0.2, and a vertical line is drawn through this point, the two points of intersection would be 11.3° and 191.3°. In radians, they would be 0.197 and 3.339.