What is the purpose of trigonometric identities

In summary, trig identities are useful in various fields such as science, engineering, law, and business. They simplify problems and are crucial for understanding complex topics. While the process of proving them may seem difficult, it teaches logical thinking skills and is only necessary once. The real value lies in applying these identities in practical situations.
  • #1
chound
164
0
As I rack my brains to solve(or atleast pretending) to prove Trig identites. What is it application in real life? :cry:
 
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  • #2
chound said:
What is it application in real life? :cry:
They exist. They simplify. Receive&understand them with joy&adulation.
 
  • #3
What do you mean by "real life"? If you intend to spend the rest of your "real life" flipping burgers, then they are of no use at all. If you think you might, at some time in your life, be working in the sciences, they they are crucially important for simplifying a huge number of problems. If you are thinking of being an engineer, an auto mechanic, or a plumber, once again, problems involving trig functions or ratios are going to loom large, and those identities will simplify them. If you think you might be a lawyer, a business man, or a writer, science and engineering will still play a large part in your life. If you want to know what's going on there, it's a really good idea to know the basics of them- and trig functions and identities are part of the basics.

In any case, the purpose of education is not so much to teach you "facts" and "identities" as it is to teach you to think. The logical discipline involved in working with and proving trig identities is one form of that. (Just like insisting that you organize your thoughts, write "topic sentenses", cite facts, and give reference in research papers.)
 
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  • #4
proving is just the hard part and you really only need to do it once. It's not really proving them that is useful but actuallying using the trig idientities are what is useful.
 

1. What are trigonometric identities?

Trigonometric identities are equations that relate different trigonometric functions to each other. They are used to simplify or solve trigonometric equations.

2. Why are trigonometric identities important?

Trigonometric identities are important because they allow us to solve complex trigonometric equations and problems more easily. They also help us to better understand and visualize the relationships between different trigonometric functions.

3. How are trigonometric identities derived?

Trigonometric identities are derived using algebraic manipulation and properties of trigonometric functions. They can also be derived using geometric relationships between angles and sides in a right triangle.

4. What is the purpose of using trigonometric identities?

The purpose of using trigonometric identities is to simplify and solve trigonometric equations and problems. They can also be used to prove other mathematical theorems and relationships.

5. What are some common trigonometric identities?

Some common trigonometric identities include the Pythagorean identity, sum and difference identities, double angle identities, and half angle identities. These are just a few examples, as there are many more identities that exist in trigonometry.

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