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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.
Seven seconds after launch of STS-121, the countdown clock at LC-39 at the Kennedy Space Center seen counting up, rather than down. In the context of a rocket launch, the "L minus Time" is the physical time before launch, e.g. "L minus 3 minutes and 40 seconds".
Secretions of various hormones, including renin, growth hormone, and prolactin, correlate positively with delta-wave activity, while secretion of thyroid-stimulating hormone correlates inversely. [3] Heart rate variability , well known to increase during REM, predictably also correlates inversely with delta-wave oscillations over the ~90-minute ...
Functions of space, time, or any other dimension can be sampled, and similarly in two or more dimensions. For functions that vary with time, let () be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every seconds, which is called the sampling interval or sampling period.
m s −2 [L][T] −2: Spatial position Position of a point in space, not necessarily a point on the wave profile or any line of propagation d, r: m [L] Wave profile displacement Along propagation direction, distance travelled (path length) by one wave from the source point r 0 to any point in space d (for longitudinal or transverse waves) L, d, r
A negative frequency causes the sin function (violet) to lead the cos (red) by 1/4 cycle. The ambiguity is resolved when the cosine and sine operators can be observed simultaneously, because cos(ωt + θ) leads sin(ωt + θ) by 1 ⁄ 4 cycle (i.e. π ⁄ 2 radians) when ω > 0, and lags by 1 ⁄ 4 cycle when ω < 0.
It occurs during stage 2 NREM sleep. It is the "largest event in healthy human EEG". [1] They are more frequent in the first sleep cycles. K-complexes have two proposed functions: [1] first, suppressing cortical arousal in response to stimuli that the sleeping brain evaluates not to signal danger, and second, aiding sleep-based memory ...
A modulated wave resulting from adding two sine waves of identical amplitude and nearly identical wavelength and frequency. A common situation resulting in an envelope function in both space x and time t is the superposition of two waves of almost the same wavelength and frequency: [2]