How does this trig identity work?

In summary, a trigonometric identity is a mathematical equation that relates trigonometric functions and is used to simplify expressions, solve equations, and prove theorems. To prove an identity, algebraic and trigonometric manipulations are used. The most commonly used identities include Pythagorean, double angle, sum and difference, and reciprocal identities. These identities have practical applications in fields such as navigation, engineering, and physics. It is important to understand and use trigonometric identities because they simplify calculations and have various real-life uses.
  • #1
zeion
466
1

Homework Statement



How does |sinx + cosx| = |sqrt(2)(x + (pi/4))| ?


Homework Equations





The Attempt at a Solution



Some kind of co-function identity?
 
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  • #2
hi zeion! :smile:

(have a square-root: √ and a pi: π :wink:)

do you mean |sinx + cosx| = |√2 sin(x + π/4)| ?

hint: expand sin(x + π/4) :wink:
 

1. What is a trigonometric identity?

A trigonometric identity is a mathematical equation that expresses a relationship between trigonometric functions. It is used to simplify expressions, solve equations, and prove other mathematical theorems.

2. How do I prove a trigonometric identity?

To prove a trigonometric identity, you need to manipulate the given equation using algebraic rules and trigonometric properties until both sides of the equation are equal. This process is known as using the "fundamental identities" or "trigonometric identities."

3. What are the most commonly used trigonometric identities?

The most commonly used trigonometric identities are the Pythagorean identities, double angle identities, sum and difference identities, and reciprocal identities. These identities are used to simplify expressions and solve equations.

4. Can I use trigonometric identities to solve real-life problems?

Yes, trigonometric identities can be used to solve real-life problems involving angles and measurements. For example, they can be used in navigation, engineering, and physics to calculate distances, heights, and other quantities.

5. Why is it important to understand and use trigonometric identities?

Trigonometric identities are essential in mathematics because they allow us to simplify complex expressions and solve equations, making calculations more manageable. They are also used in many fields such as science, engineering, and technology, making them important for practical applications.

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