sin 𝑥 and cos 𝑥 are both negative in the third quadrant. Finally, the cosine of any angle between 270 and 360 degrees is positive, whereas the sine and tangent of any angle in this quadrant is negative. Whilst we could prove these using the unit circle or the graphs of our ...
sin(θi)+sin(θo)=mλ/nΛ Eq. 1 where Eq. 1 is diffraction (or reflection or scatter) relationship between input wavelength λ, input incident angle θi, output incident angle θo, and the spatial period Λ of the grating 12. Further, m is the “order” of the reflection ...
Then, we inserted (16) in (9) and simplified the resulting substitutions to arrive at 𝐐(1,sin(𝑧),cos(𝑧),sin(𝑧)cos(𝑧),sin2(𝑧),cos(𝑧)sin2(𝑧),sin3(𝑧))2(𝐵+𝐹cos(𝑧))3=0.Q(1,sin(z),cos(z),sin(z)cos(z),sin2(z),cos(z)sin2(z),sin3(z...
This is a useful and general method for calculating the mean phase. The circular mean of a set of angles (ai, i = 1…n) is defined as 𝑎𝑚=arg(𝑋,𝑌) 𝑤𝑖𝑡ℎ 𝑋=∑𝑖=1𝑛cos(𝑎𝑖) and 𝑌=∑𝑖=1𝑛sin(𝑎𝑖)am=arg(X,Y) with X=∑i=1ncos(ai...
𝑦𝑖=−(𝑌𝑖−𝑌0)sin𝛽+(𝑋𝑖−𝑋0)cos𝛽yi=−(Yi−Y0)sinβ+(Xi−X0)cosβ (6) The positive value of the angle β occurs when the system is rotated to the left. In the local coordinate system, the linear coordinate Li determined by the Formula (2) sti...