$\sin^2{\theta}+\cos^2{\theta} \,=\, 1$

The sum of the squares of sine and cosine functions at an angle equals to one is called the Pythagorean identity of sine and cosine functions.

The sine and cosine are two functions in trigonometry. They have a direct relationship between them in square form but it represents the Pythagorean theorem. Hence, the relationship between sine and cosine functions in square form is called the Pythagorean identity of sine and cosine functions.

- $\Delta BAC$ is a right triangle and its angle is denoted by theta.
- The sine and cosine functions are written as $\sin{\theta}$ and $\cos{\theta}$ respectively.
- Their squares are mathematically written as $\sin^2{\theta}$ and $\cos^2{\theta}$ respectively.

The sum of them is equal to one and it is called the Pythagorean identity of sine and cosine functions.

$\sin^2{\theta}+\cos^2{\theta} \,=\, 1$

The Pythagorean identity of sine and cosine functions is also written popularly in two other forms.

- $\sin^2{x}+\cos^2{x} \,=\, 1$
- $\sin^2{A}+\cos^2{A} \,=\, 1$

Remember, the angle of right triangle can be denoted by any symbol but the relation between sine and cosine functions should be expressed in that symbol.

Learn how to derive the Pythagorean identity of sine and cosine functions in mathematical form by geometrical method.

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved