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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 ...
Bible Gateway's engagement features include the ability to display a single Bible verse in many English Bible translations, the ability to display and compare up to five Bible translations side by side at once, its daily Blog, more than 60 email devotions, Bible reading plans and verses-of-the-day, a free mobile app, audio Bibles, video ...
In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity ...
Identity 1: + = The following two results follow from this and the ratio identities. To obtain the first, divide both sides of + = by ; for the second, divide by .
A trigonometric polynomial can be considered a periodic function on the real line, with period some divisor of , or as a function on the unit circle.. Trigonometric polynomials are dense in the space of continuous functions on the unit circle, with the uniform norm; [4] this is a special case of the Stone–Weierstrass theorem.
By John Kruzel. WASHINGTON (Reuters) -The U.S. Supreme Court declined on Monday to decide whether federally mandated warnings on cigarette packs that graphically illustrate the health risks of ...
Three people were shot and one person was stabbed following what authorities believe to be a family dispute at a restaurant in the Phoenix Sky Harbor International Airport.
In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions.Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely and and then integrated.