Properties Of Inverse Trigonometric Functions
Chapter Name : Inverse Trigonometric Functions |
Sub Topic Code : 104_12_02_03_01 |
Topic Name : Properties Of Inverse Trigonometric Functions |
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Sub Topic Name : Properties Of Inverse Trigonometric Functions |
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Introduction
In this topic we prove some important properties of inverse trigonometric functions. These results are valid within the principal value branches of the corresponding inverse trigonometric functions and wherever they are defined. These properties can be used to solve numerous inverse trigonometric problems by making them easier.
Pre-Requisites:
• Trigonometric Functions • Concepts of Domain and Range of a Functions • Graphical Representation of Trigonometric Functions
Activity:
recording studio in your neighborhood
Real Life Question:
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Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Range | The range of a function refers to either the co-domain or the image of the function, depending upon usage. The co-domain is a set containing the function's output, whereas the image is only the part of the co-domain where the elements are outputs of the function. |
| Domain | The domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined. |
| Trigonometric Functions | The trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. |
| Inverse trigonometric Functions | The inverse trigonometric functions (occasionally called cyclometric functions) are the inverse functions of the trigonometric functions with suitably restricted domains. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Inverse Trigonometric Functions charts | To know about Inverse Trigonometric Functions |
Real life uses :
Digital imaging is a real life application of trigonometry. Computer generation of complex imagery is made possible by the use of geometrical patterns that define the precise location and color of each of the infinite points on the image to be created. The image is made detailed and accurate by a technique referred to as triangulation. The edges of the triangles that form the image make a wire frame of the object to be created and contribute to a realistic picture.
Places to visit :
Visit a music recording studio in your neighborhood and observe the different patterns made by the music being played.
Practical examples around us
| Examples | Explainations |
|---|---|
| Trigonometry can be used to measure the heights of mountains | We measure mountains because this information is of great value for aircraft designing and navigation. Also those people with medical conditions that prevent them from traveling to very high altitudes need to know the altitudes they will be travelling at so as to be sure that it’s safe for travel. |
What you learn in Theory:
We learn trigonometric properties and the steps required to prove them.
What you learn in Practice:
We learn how to use these properties to solve complex inverse trigonometric problems.