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)
“So long as the source of our identity is external—vested in how others judge our performance at work, or how others judge our children’s performance, or how much money we make—we will find ourselves hopelessly flawed, forever short of the ideal.”
—Melinda M. Marshall (20th century)