Pythagorean Identity
The basic relationship between the sine and the cosine is the Pythagorean trigonometric identity:
where cos2 θ means (cos(θ))2 and sin2 θ means (sin(θ))2.
This can be viewed as a version of the Pythagorean theorem, and follows from the equation x2 + y2 = 1 for the unit circle. This equation can be solved for either the sine or the cosine:
Read more about this topic: List Of Trigonometric Identities
Famous quotes containing the words pythagorean and/or identity:
“Come now, let us go and be dumb. Let us sit with our hands on our mouths, a long, austere, Pythagorean lustrum. Let us live in corners, and do chores, and suffer, and weep, and drudge, with eyes and hearts that love the Lord. Silence, seclusion, austerity, may pierce deep into the grandeur and secret of our being, and so diving, bring up out of secular darkness, the sublimities of the moral constitution.”
—Ralph Waldo Emerson (1803–1882)
“During the first formative centuries of its existence, Christianity was separated from and indeed antagonistic to the state, with which it only later became involved. From the lifetime of its founder, Islam was the state, and the identity of religion and government is indelibly stamped on the memories and awareness of the faithful from their own sacred writings, history, and experience.”
—Bernard Lewis, U.S. Middle Eastern specialist. Islam and the West, ch. 8, Oxford University Press (1993)