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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 ...
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Sec-1, SEC-1, sec-1, or sec −1 may refer to: . sec x−1 = sec(x)−1 = exsec(x) or exsecant of x, an old trigonometric function; sec −1 y = sec −1 (y), sometimes interpreted as arcsec(y) or arcsecant of y, the compositional inverse of the trigonometric function secant (see below for ambiguity)
The confusion is somewhat mitigated by the fact that each of the reciprocal trigonometric functions has its own name — for example, (cos(x)) −1 = sec(x). Nevertheless, certain authors advise against using it, since it is ambiguous.
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 ...
A 25-year-old Alabama resident named Eric Council Jr. was arrested Thursday morning in connection with the unauthorized takeover of the Security and Exchange Commission’s X account in January ...
In calculus, the integral of the secant function can be evaluated using a variety of methods and there are multiple ways of expressing the antiderivative, all of which can be shown to be equivalent via trigonometric identities,
Speaking of period romances (there are a bunch on this list, I regret nothing), the first (technically illegal) same-sex matrimony in Spain is imagined as the most epic love story of all time.