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teddyw123 · Jul 17, 2012, 12:40 PM

The Pythagorean Theorem gives the relationship between the sides of a right triangle. The following identities show the relationships between the trigonometric functions of a particular angle.
sin^2 θ + cos^2 θ = 1
tan^2 θ + 1 = sec^2 θ
1 + cot^2 θ = csc^2 θ

Why then are these referred to as the Pythagorean Identities?

Is the answer to this question:
because they are showing and proving the Pythadorean theorum through trigonometry? I'm not sure how else to answer this...

ali18ninja · Jul 18, 2012, 02:56 AM

They show the basic relations between the sine and cosine functions, from which all others may be derived.

ebaines · Jul 18, 2012, 07:42 AM

Just to add an example: if the two legs of a right angle triangle are A and B and the hypotenuse is C, then Pythagorus says that $A^2 + B^2 = C^2$ . Now consider as an example the second equation you wrote: $tan^2 \theta + 1 = sec^2 \theta$ :

$<br /> tan^2 \theta + 1 = \frac {A^2}{B^2} + 1 = \frac {A^2 + B^2}{B^2} = \frac {C^2}{B^2} = sec^2 \theta<br />$