Pythagorean Identity (sin/cos)1=
The Pythagorean Identity is a fundamental trigonometric identity that relates the sine and cosine functions with any angle in a right triangle
The Pythagorean Identity is a fundamental trigonometric identity that relates the sine and cosine functions with any angle in a right triangle. The identity states that for any angle in a right triangle, the square of the sine of the angle added to the square of the cosine of the angle is always equal to one.
Mathematically, the Pythagorean Identity is expressed as:
sin^2(theta) + cos^2(theta) = 1
In this identity, theta represents an angle in the right triangle, sin(theta) represents the sine of the angle, and cos(theta) represents the cosine of the angle.
The Pythagorean Identity is derived from the Pythagorean Theorem, which 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. By applying this theorem to the trigonometric ratios of sine and cosine in a right triangle, we get the Pythagorean Identity.
This identity is not only important in trigonometry but also in many other fields of mathematics and science, as it provides a strong connection between two fundamental trigonometric functions. It is used extensively in solving trigonometric equations, simplifying expressions, and proving other trigonometric identities.
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