Pythagorean trigonometric identity

As Trigonometric Pythagoras is the identity

Referred to. This stands for and for. The validity of this identity can be shown on the unit circle, with the help of the theorem of Pythagoras, who is also the namesake for this commonly used set of trigonometry.

Derivation

The basis of the Pythagorean theorem is used. He says that in a right triangle and with the hypotenuse and the other sides

Applies. If the angle selected in said right-angled triangle such that its opposite side and its adjacent side is, so is generally

Inserting both equations in the Pythagorean theorem then gives

Geometric illustration

The adjacent sketch is the unit circle, ie a circle with radius 1, and a signal generated by the circuit shown right-angled triangle. Applying the Pythagorean theorem immediately shows the validity of the trigonometric Pythagoras.