6.2. Pythagorean Identities http://www.ck12.org
6.2 Pythagorean Identities
Here you will prove and use the Pythagorean identities for the six trigonometric functions to simplify expressions
and write proofs.
The Pythagorean Theorem works on right triangles. If you consider thexcoordinate of a point along the unit circle to
be the cosine and theycoordinate of the point to be the sine and the distance to the origin to be 1 then the Pythagorean
Theorem immediately yields the identity:
y^2 +x^2 = 1
sin^2 x+cos^2 x= 1An observant student may guess that other Pythagorean identities exist with the rest of the trigonometric func-
tions. Is tan^2 x+cot^2 x=1 a legitimate identity?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61317http://www.youtube.com/watch?v=OmJ5fxyXrfg James Sousa: Fundamental Identities: Reciprocal, Quotient, Pythagorean
Guidance
The proof of the Pythagorean identity for sine and cosine is essentially just drawing a right triangle in a unit circle,
identifying the cosine as thexcoordinate, the sine as theycoordinate and 1 as the hypotenuse.