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Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
Depiction of the sin of Adam and Eve (The Garden of Eden with the Fall of Man by Jan Brueghel the Elder and Pieter Paul Rubens). Original sin (Latin: peccatum originale) in Christian theology refers to the condition of sinfulness that all humans share, which is inherited from Adam and Eve due to the Fall, involving the loss of original righteousness and the distortion of the Image of God. [1]
A prominent Methodist catechism, "A Catechism on the Christian Religion: The Doctrines of Christianity with Special Emphasis on Wesleyan Concepts" contrasts original sin and actual sin: [3] Original sin is the sin which corrupts our nature and gives us the tendency to sin. Actual sins are the sins we commit every day before we are saved, such ...
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.According to the law, = = =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.
The red section on the right, d, is the difference between the lengths of the hypotenuse, H, and the adjacent side, A.As is shown, H and A are almost the same length, meaning cos θ is close to 1 and θ 2 / 2 helps trim the red away.
Dexter: Original Sin is set in 1991 Miami just as young Dexter Morgan is set to begin his career as a forensics analyst at the Miami Metro Police Department. It's right around this time that ...
The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles , see Trigonometric functions . Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine , or on the differential equation f ″ + f = 0 ...
which by the Pythagorean theorem is equal to 1. This definition is valid for all angles, due to the definition of defining x = cos θ and y sin θ for the unit circle and thus x = c cos θ and y = c sin θ for a circle of radius c and reflecting our triangle in the y-axis and setting a = x and b = y.