Introduction
Chapter Name : Inverse Trigonometric Functions |
Sub Topic Code : 104_12_02_01_01 |
Topic Name : Introduction |
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Sub Topic Name : Introduction |
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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 Function. • Graphical Representation of Trigonometric Functions.
Activity:
Use a measuring tape to find the shadow of a building. Also find its line of sight. Then, use inverse trigonometric identities to find out the angle of elevation.
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 |
|---|---|
| Measuring Tape | Use a measuring tape to find the shadow of a building. Also find its line of sight. Then, use inverse trigonometric identities to find out the angle of elevation. |
Real life uses :
It is used in navigation to find the distance of the shore from a point in the sea. Trigonometry is also commonly used in finding the height of towers and mountains.
Places to visit :
Use the Inverse trigonometric identities to find out different light angles in your home.
Practical examples around us
| Examples | Explainations |
|---|---|
| Navigation in Oceans | It is used in oceanography in calculating the height of tides in oceans. |
| Distance between planets | It is used in finding the distance between celestial bodies. |
What you learn in Theory:
Identifying the formulas, domain and range 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.