Inverse Trigonometric Functions “The power of Mathematics is often to change one thing into another, to change geometry into language” - Marcus du Sautoy John F.W. Herschel Fig. . ( , x y Slope: m Inverse - - Illustration- ( Movie Theatre Screens ) Suppose that a movie theatre has a screen of metres tall.
When someone sits down, the bottom of the screen is metres above the eye level. The angle formed by drawing a line from the eye to the bottom of the screen and a line from the eye to the top of the screen is called the viewing angle. In Fig. .
, θ is the viewing angle. Suppose that the person sits x metres away from the screen. The viewing angle θ is given by the function θ ( ) − Observe that the viewing angle θ is a function of x . Illustration- ( Drawbridge ) Assume that there is a double-leaf drawbridge as shown in Fig.
. . Each leaf of the bridge is metres long. A ship of metres wide needs to pass through the bridge.
Inverse trigonometric function helps us to find the minimum angle θ so that each leaf of the bridge should be opened in order to ensure that the ship will pass through the bridge. In class XI, we have discussed trigonometric functions of real numbers using unit circle, where the angles are in radian measure. In this chapter, we shall study the inverse trigonometric functions, their graphs and properties. In our discussion, as usual and stand for the set of all real numbers and all integers, respectively.
Let us recall the definition of periodicity, domain and range of six trigonometric functions.