Pythagorean Identitycos² θ=
The Pythagorean identity related to cosine is:
cos²θ + sin²θ = 1
This identity is derived from the Pythagorean theorem in geometry
The Pythagorean identity related to cosine is:
cos²θ + sin²θ = 1
This identity is derived from the Pythagorean theorem in geometry. In a right triangle, the Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
By considering a right triangle with angle θ, where the adjacent side has length adjacent = cosθ and the opposite side has length opposite = sinθ, we can apply the Pythagorean theorem:
(hypotenuse)² = (adjacent)² + (opposite)²
Substituting in the values, we have:
1 = cos²θ + sin²θ
Hence, this equation holds true for any angle θ, and it is known as the Pythagorean identity. It is a fundamental identity in trigonometry and is often used to simplify trigonometric expressions or solve trigonometric equations.
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