Master Trigonometric Identities with Double Angle Techniques

In summary, a trigonometric identity is an equation that relates trigonometric functions and is useful for simplifying and solving trigonometric equations. These identities are important because they allow for manipulation and simplification of complex expressions, and can be proven using various methods. Some commonly used identities include the Pythagorean identities, sum and difference formulas, double angle formulas, and half angle formulas, and they have many real-world applications in fields such as navigation, surveying, and engineering.
  • #1
Mrencko
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IMG_20150506_165135408.jpg
I am doig trigonometric identities and i got this one, (all will be in the picture the solution and my work) i used the double angle for this but i am afraid i didn't get the exact idea, just guessing, good guessing, so i want to know how is the proper way to reach the solution
 
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  • #2
Here is a little bigger view for folks.

upload_2015-5-6_18-28-10.png


So, I take it that you want to simplify ##\ \sqrt{1+\cos(6\theta)\,}\ ## using the double angle identity for cosine.

Write 6θ as 2(3θ) .
 
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1. What is a trigonometric identity?

A trigonometric identity is an equation that expresses the relationship between trigonometric functions, such as sine, cosine, and tangent. These identities are true for all values of the variables involved and are used to simplify and solve trigonometric equations.

2. Why are trigonometric identities important?

Trigonometric identities are important because they allow us to manipulate and simplify complex trigonometric expressions, making it easier to solve equations and work with trigonometric functions in various applications, such as physics, engineering, and mathematics.

3. How can I prove a trigonometric identity?

There are several methods for proving a trigonometric identity, such as using algebraic manipulation, using geometric proofs, or using the sum and difference formulas for trigonometric functions. It is important to understand the properties and rules of trigonometric functions to effectively prove identities.

4. What are the most commonly used trigonometric identities?

Some of the most commonly used trigonometric identities include the Pythagorean identities, sum and difference formulas, double angle formulas, and half angle formulas. These identities are used to simplify expressions and solve equations involving trigonometric functions.

5. How can I use trigonometric identities in real-world applications?

Trigonometric identities are used in various real-world applications, such as navigation, surveying, and engineering. For example, in navigation, trigonometric identities are used to calculate distances and angles between points on a map. In engineering, they are used to design and construct buildings, bridges, and other structures.

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