Trigonometric Equations
Chapter Name : Trigonometric Functions |
Sub Topic Code : 104_11_03_05_01 |
Topic Name : Trigonometric Equations |
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Sub Topic Name : Trigonometric Equations |
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Introduction
All the trigonometric functions repeat themselves after an interval of 2? and some even after ?. This leads to the concept of general solution, which combines all the possible solutions.
Pre-Requisites:
Angles, definition of trigonometric functions, their domain and range, graph of the trigonometric functions.
Real Life Question:
Sin (?/3) = sin (2?/3) then if sin x = ?3/2 then x is what, ?/3 or 2?/3.
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Sine | In a right triangle, it is the ratio of the perpendicular to the hypotenuse. |
| Cosine | In a right triangle, it is the ratio of the base to the hypotenuse |
| Tangent | In a right triangle, it is the ratio of perpendicular to the base. |
| General solution | Combination of all the solution in a generalized manner. |
| Principal solution | Only those solutions that are in the range 0 < x <2?. |
Learning aids / Gadgets
| Gadgets | How it can be used |
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Real life uses :
Using the periodicity of the trigonometric function we can find the value of these function up to millions of degrees.
Practical examples around us
| Examples | Explainations |
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What you learn in Theory:
What are general and principal solutions? How to get general solution from principal solution? How to solve the trigonometric equations?