sin^2x+cos^2x=
The equation sin^2x + cos^2x = 1 is a fundamental trigonometric identity known as the Pythagorean identity
The equation sin^2x + cos^2x = 1 is a fundamental trigonometric identity known as the Pythagorean identity. This identity holds true for any angle x in the domain of trigonometric functions.
To understand why this equation is true, let’s break it down:
The sine squared (sin^2x) represents the square of the sine of angle x. It is calculated by squaring the value of sin(x). Similarly, cos^2x represents the square of the cosine of angle x, obtained by squaring the value of cos(x).
The Pythagorean identity states that the sum of the squares of sine and cosine of any angle is always equal to 1. In other words, no matter what angle x you choose, when you square the sine of x and add it to the square of the cosine of x, you will always get 1.
This identity is significant in trigonometry because it allows us to manipulate trigonometric equations and simplify them. It comes from the relationship between the sides of a right triangle and the unit circle. In a unit circle, the radius is 1, and we can define the sine and cosine of an angle in terms of the coordinates of a point on the circle. The Pythagorean identity emerges from the Pythagorean theorem applied to the right triangle formed within the unit circle.
In summary, sin^2x + cos^2x = 1 is a fundamental trigonometric identity that establishes the relationship between the squares of the sine and cosine of any angle x.
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