Basic Concepts
Chapter Name : Inverse Trigonometric Functions |
Sub Topic Code : 104_12_02_02_01 |
Topic Name : Basic Concepts |
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Sub Topic Name : Basic Concepts |
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Introduction
The inverse trigonometric functions (occasionally called cyclometric functions) are the inverse functions of the trigonometric functions with suitably restricted domains. The notations sin?1, cos?1, tan?1, etc. are often used for arcsin, arccos, arctan, etc. The ranges of the inverse functions are proper subsets of the domains of the original functions.
Pre-Requisites:
• Trigonometric Functions • Concepts of Domain and Range of a Functions • Graphical Representation of Trigonometric Functions
Activity:
Observe different graph patterns in your natural surroundings like sine and cosine patterns in soundtracks (music).
Real Life Question:
Find the height of towers and mountains by calculating angles suspended between them and their shadows and the length of the shadows.
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| 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. |
| 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. |
| 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. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Graphs | Plot different inverse trigonometric functions on graphs and try to see the different patterns on. |
Real life uses :
Sound travels in waves and this pattern though not as regular as a sine or cosine function, is still useful in developing computer music. A computer cannot listen to and comprehend music as human beings do, so computers represent it mathematically by its constituent sound waves. This means that sound engineers and technologists who research advances in computer music and even hi-tech music composers have to relate to the basic laws of trigonometry.
Practical examples around us
| Examples | Explainations |
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What you learn in Theory:
Plotting the graphs and identifying principal value branches, domains and ranges of Inverse Trigonometric functions.
What you learn in Practice:
Use inverse trigonometric identities to find out the angle of elevation for trees, buildings, towers etc.