Understanding the Pythagorean Identity | The Relationship between Sine and Cosine in Trigonometry

sin^2x + cos^2x =

The equation “sin^2x + cos^2x =” is an identity in trigonometry known as the Pythagorean identity

The equation “sin^2x + cos^2x =” is an identity in trigonometry known as the Pythagorean identity. It states that the sum of the squares of the sine and cosine of an angle (x) is always equal to 1.

sin^2x + cos^2x = 1

This identity holds true for all values of x, regardless of the angle’s size or sign. It is a fundamental relationship between the sine and cosine functions in a right triangle, where the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) according to the Pythagorean theorem:

a^2 + b^2 = c^2

In the context of the unit circle, this identity shows that the values of sine and cosine are always related in such a way that when squared and added together, they yield a constant value of 1. This relationship is a fundamental principle in trigonometry and has numerous applications in various fields of science and mathematics.

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