Trigonometric identities are powerful tools for simplifying complex equations in math and science. Three core groups—reciprocal, quotient, and Pythagorean—form the foundation.

That roadblock has now been cleared by two U.S. high school students who flipped the problem on its head and produced new trigonometric proofs that stand up to expert scrutiny. Their story began with ...

An interval-valued Pythagorean hesitant fuzzy set (IVPHFS) not only can be regarded as the union of some interval-valued Pythagorean fuzzy sets but also represent the Pythagorean hesitant fuzzy ...

Normal fuzzy sets and Pythagorean cubic fuzzy sets are the best means to deal with fuzziness. Combining both of these structures in our current work, we establish the idea of Pythagorean cubic normal ...

Popular Mechanics said they used the Law of Sines while avoiding the Pythagorean theorem’s trigonometric identity (sin²α + cos²α = 1).

Ne’Kiya Jackson and Calcea Johnson have published a paper on a new way to prove the 2000-year-old Pythagorean theorem. Their work began in a high school math contest.

Ne’Kiya Jackson and Calcea Johnson have published a paper on a new way to prove the 2000-year-old Pythagorean theorem. Their work began in a high school math contest.

Using a trigonometry rule called the Law of Sines, the students showed that the "proof is independent of the Pythagorean trig identity sin2x + cos2x = 1." ...

2 US teens solve impossible 2,000-year-old Pythagorean Theorem with trigonometry Their groundbreaking work includes not just one, but nine new proofs of the Pythagorean theorem using trigonometry.

In a new peer-reviewed study, Ne'Kiya Jackson and Calcea Johnson outlined 10 ways to solve the Pythagorean theorem using trigonometry, including a proof they discovered in high school.