sin^2(theta)+cos^2(theta) =
The equation sin^2(theta) + cos^2(theta) = 1 is known as the Pythagorean Identity in trigonometry
The equation sin^2(theta) + cos^2(theta) = 1 is known as the Pythagorean Identity in trigonometry. It represents a fundamental relationship between the sine (sin) and cosine (cos) functions of an angle theta.
In a right-angled 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. In terms of trigonometric functions, if we consider an angle theta in the triangle, the sine of theta is defined as the ratio of the length of the side opposite theta to the hypotenuse, and the cosine of theta is defined as the ratio of the length of the adjacent side to the hypotenuse.
Using these definitions, we can express the Pythagorean theorem in terms of trigonometric functions. The square of the length of the side opposite theta, which is sin^2(theta), plus the square of the length of the adjacent side, which is cos^2(theta), is equal to the square of the hypotenuse. Therefore, sin^2(theta) + cos^2(theta) = 1.
This identity is extremely useful in various trigonometric calculations and proofs. It showcases the interrelationship between sine and cosine, and demonstrates how their values are constrained by the unit circle.
More Answers:
How to Find the Derivative of csc x Using the Quotient RuleSimplifying the Equation | tan^2(theta) + 1 = sec^2(theta)
Exploring the Derivative of Tan x | Trigonometric Definition and Sec^2 x Connection