What is an example of the Pythagorean Identity?

\sin^2(\theta) + \cos^2(\theta) = 1

Pythagorean Identity | Math Rules | Equation Encyclopedia

Q: What should I remember about the Pythagorean Identity?

This identity is valid for all real numbers \theta. It is fundamental for deriving many other trigonometric relationships and simplifying expressions.

The rule

Description

The Pythagorean Identity is a fundamental trigonometric identity stating that the sum of the squares of the sine and cosine of an angle is equal to one. It is a direct consequence of the Pythagorean theorem applied to a right-angled triangle or the unit circle. This identity holds true for all real values of the angle.

See it in action

Examples

1

$sin^{2}$ ( $θ$ ) + $cos^{2}$ ( $θ$ ) = 1

2

$sin^{2}$ (45^ $\circ$ ) + $cos^{2}$ (45^ $\circ$ ) = \left(\frac{√(2)}{2}\right)^2 + \left(\frac{√(2)}{2}\right)^2 = $\frac{1}{2}$ + $\frac{1}{2}$ = 1

Good to know

Key Facts

This identity is valid for all real numbers $θ$ .
It is fundamental for deriving many other trigonometric relationships and simplifying expressions.

Common questions

Frequently Asked Questions

The Pythagorean Identity is a fundamental trigonometric identity stating that the sum of the squares of the sine and cosine of an angle is equal to one. It is a direct consequence of the Pythagorean theorem applied to a right-angled triangle or the unit circle. This identity holds true for all real values of the angle.

$sin^{2}$ ( $θ$ ) + $cos^{2}$ ( $θ$ ) = 1

This identity is valid for all real numbers $θ$ . It is fundamental for deriving many other trigonometric relationships and simplifying expressions.