Trigonometry, plane between

The trigonometric functions of angles are the ratios between the various sides of the reference triangles shown in Fig. 3-38 for the various quadrants. Clearly r = Vx2 + y2 > 0. The fundamental functions (see Figs. 3-39, 3-40, 3-41) are Plane Trigonometry... 

It is easy to show, using elementary trigonometry, that the pyramidality coefficient of a given atom is a function of its distance, PD, from the plane defined by three substituents attached to this atoms. A simplified form of such a function may be derived subject to the assumption that the bond lengths, D, between the considered atom and... 

Calculate the width of the peptide plane, that is, (a) the distance x, between the a-carbon and the oxygen, and (b) the distance, y, between the H attached to the nitrogen atom and the a-carbon. Consult Figure 2-1. (Hint use plane trigonometry.)... 

In the diagram opposite, an ordered array of atoms is represented simply by black dots. Consider the two waves of incident radiation (angle of incidence = 0) to be in-phase. Let one wave be reflected from an atom in the first lattice plane and the second wave be reflected by an atom in the second lattice plane as shown in the diagram. The two scattered waves will only be in-phase if the additional distance travelled by the second wave is equal to a multiple of the wavelength, i.e. n. If the lattice spacing (i.e. the distance between the planes of atoms in the crystal) is d, then by simple trigonometry, we can see from the diagram opposite that ... 

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