Question

Relate the *Pythagorean theorem* to the *distance formula* to *trigonometric identities*.

Accepted Answer

The **Pythagorean theorem**, which relates the side lengths of a right triangle to its hypotenuse, is defined as $$a^2 + b^2 = c^2$$, where *a* and *b* are the side lengths, and *c* is the hypotenuse.   

The **distance formula**, defined as $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$, is the Pythagorean formula applied to a coordinate plane.

The **trigonometric identity**, $$\cos^2\;	heta + \sin^2\;	heta = 1$$, is based on the *unit circle* (with radius 1), where *cosine* represents the *x* side length and *sine* represents the *y* side length.    Similarly, $$1 + 	an^2\;	heta = \sec^2\;	heta$$, and $$\cot^2\;	heta + 1 = \csc^2\;	heta$$ derive from the same principle.

Flashcard 6 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

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