Proving the Pythagorean Theorem: The Relationship Between Sine and Cosine

  • Thread starter Mattara
  • Start date
In summary, the conversation is about the English word for a specific rule in mathematics, known as the Pythagorean identity. The speakers mention that it is commonly referred to as one of the most famous trigonometric identities and can be found in lists titled as such. They also discuss the name of this rule in different languages, with one speaker mentioning it as "Idiotformelen" in Danish and the other suggesting "trigonometriska ettan" or "(the) trigonometry 1" in their native language.
  • #1
Mattara
348
1
What is the English word for this rule? It doesn't sound right if I do a direct translation and google didn't turn up much.

Thank you :smile:
 
Physics news on Phys.org
  • #2
(One of) The most famous trigonometric identity? ;) You'll generally find it in a list titled that way.
 
  • #3
I think it's called the Pythagorean identity.
 
  • #5
Thanks a lot, both of you. The name for it in my native language has been highly influenced by the number "1" :/
 
  • #6
What would it be called in your native language? In Danish it is readily called "Idiotformelen" -- the idiot formula...
 
  • #7
That was funny. It would be "trigonometriska ettan" or "(the) trigonometry 1"
 

1. What is the Pythagorean Theorem?

The Pythagorean Theorem is a mathematical principle that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

2. How is the Pythagorean Theorem proven?

The Pythagorean Theorem can be proven using various methods, including algebraic, geometric, and trigonometric proofs. One of the most commonly used proofs involves using the relationships between sine, cosine, and the sides of a right triangle.

3. What is the relationship between sine and cosine in the Pythagorean Theorem?

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, while the cosine of an angle is equal to the length of the side adjacent to the angle divided by the length of the hypotenuse. This relationship can be used to prove the Pythagorean Theorem.

4. Can the Pythagorean Theorem be used in non-right triangles?

No, the Pythagorean Theorem can only be applied to right triangles. In non-right triangles, the Law of Cosines and Law of Sines are used to find missing side lengths or angles.

5. How is the Pythagorean Theorem used in real life?

The Pythagorean Theorem has many real-life applications, such as in construction and engineering for calculating distances and angles. It is also used in navigation, astronomy, and other fields that involve measuring distances and angles.

Similar threads

  • Calculus and Beyond Homework Help
Replies
1
Views
1K
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
547
  • Topology and Analysis
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • STEM Career Guidance
Replies
3
Views
1K
Replies
22
Views
969
  • Calculus and Beyond Homework Help
Replies
29
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
1K
Replies
10
Views
608
Back
Top