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In April 2023, a study investigated four extremely redshifted objects discovered by the James Webb Space Telescope. [5] Their study suggested that three of these four, namely JADES-GS-z13-0, JADES-GS-z12-0, and JADES-GS-z11-0, are consistent with being point sources, and further suggested that the only point sources which could exist in this time and be bright enough to be observed at these ...
Dark star (Newtonian mechanics), a star that has a gravitational pull strong enough to trap light under Newtonian gravity Dark star (dark matter), a star heated by annihilation of dark matter particles within it
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.
A dark star, therefore, has a rarefied atmosphere of "visiting particles", and this ghostly halo of matter and light can radiate, albeit weakly. Also as faster-than-light speeds are possible in Newtonian mechanics, it is possible for particles to escape. Radiation effects A dark star may emit indirect radiation as described above.
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 θ < θ. So we have < <. For negative values of θ we have, by the symmetry of the sine function
The mathematics of trigonometry and exponentials are related but not exactly the same; exponential notation emphasizes the whole, whereas cis x and cos x + i sin x notations emphasize the parts. This can be rhetorically useful to mathematicians and engineers when discussing this function, and further serve as a mnemonic (for cos + i sin ).
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.
In optics, Lambert's cosine law says that the observed radiant intensity or luminous intensity from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal; I = I 0 cos θ. [1] [2] The law is also known as the cosine ...