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The linear combination, or harmonic addition, of sine and cosine waves is equivalent to a single sine wave with a phase shift and scaled amplitude, [33] [34] a cos x + b sin x = c cos ( x + φ ) {\displaystyle a\cos x+b\sin x=c\cos(x+\varphi )}
Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.
This geometric argument relies on definitions of arc length and area, which act as assumptions, so it is rather a condition imposed in construction of trigonometric functions than a provable property. [2] For the sine function, we can handle other values. If θ > π /2, then θ > 1. But sin θ ≤ 1 (because of the Pythagorean identity), so sin ...
A standard method of evaluating the secant integral presented in various references involves multiplying the numerator and denominator by sec θ + tan θ and then using the substitution u = sec θ + tan θ. This substitution can be obtained from the derivatives of secant and tangent added together, which have secant as a common factor. [6]
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.
SI derived units are units of measurement derived from the seven SI base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem).
The joule-second also appears in quantum mechanics within the definition of the Planck constant. [2] Angular momentum is the product of an object's moment of inertia, in units of kg⋅m 2 and its angular velocity in units of rad⋅s −1. This product of moment of inertia and angular velocity yields kg⋅m 2 ⋅s −1 or the joule-second.
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)