According to the Pythagorean identity, what is sin squared plus cos squared equal to?

The Pythagorean identity is a fundamental relationship in trigonometry, expressing a special connection between the sine and cosine functions. It states that the square of the sine of an angle plus the square of the cosine of the same angle is equal to one. This can be written mathematically as:

[

\sin^2(\theta) + \cos^2(\theta) = 1

]

This identity holds true for all angles, making it a cornerstone of trigonometric principles. The reason this identity is particularly significant is because it provides a way to derive other trigonometric identities and solve problems involving angles and triangles.

For example, if you know the value of the sine or cosine of an angle, you can easily find the other by rearranging the identity. This relationship underlies much of trigonometric analysis and applications, demonstrating how these functions are interrelated.

Thus, the correct answer signifies the fundamental nature of this relationship, which is crucial for both theoretical and practical applications in mathematics and related fields.