Angles. Measurement Radian

Dispersion measures the ability to separate wavelengths differing by AX through the difference in angle. A( > (radians). For the grating in Figure 20-6, the dispersion is... 

The measurement of angles in radians is the SI standard, although the degrees-minutes-seconds format is acceptable. It is recommended, however, that degrees and decimal fractions thereof be used in which 1° is exactly equal to (17/180) rad thus, 33°45 36" becomes 33.76° in the recommended format. 

Using a calculator, find the value of the cosine of 15.5 ° and the value of the cosine of 375.5 Display as many digits as your calculator is able to display. Check to see if there is any round-off error in the last digit. Choose another pair of angles that differ by 360 ° and repeat the calculation. Set your calculator to use angles measured in radians. Find the value of sin(0.3000). Find the value of sin(0.3000 -t- 2n). See if there is any round-off error in the last digit. 

Comparison of Eqs. (2.1) and (2.7) shows that for a fairly small angle, the sine of an angle and the measure of the angle in radians are approximately equal, since the sine differs from the measure of the angle only by having the opposite side in place of the arc length, which is approximately the same size. In fact,... 

The force constants are in 10 dyn/cm, with angles measured in radians. For original references see footnote a of this table. 

A sessile drop of liquid at rest on the surface of a solid in contact with a gas comes to equilibrium with the contact angle, that is, the plane angle measured in the liquid, and denoted by the Greek letter, 0, and expressed in radians (see Figure 20.3) as... 

Why does amplitude have no dimensions Recall that amplitude is an angle measured in radians. The amplitude of an angle is the ratio of the length of a radius divided by the arc swept out by the radius. The dimensions of amplitude are thus L/L, which is dimensionless. 

Figure A10.4 (a) The coordinate system and definition of an infinitesimal volume c/r for cylindrical polar coordinates, the factor u enters dx because of the definition of an arc length using angles measured in radians, (b) A slice through the H—H bond showing the charge density on a plane perpendicular to the H2 Cco axis, (c) The geometry used to obtain the distances r and /-j from each nuclear centre these are the varieJales used in the s-orbital basis functions, since they define the nuclear-electron separations.

Explain why angle is a nondimensional quantity regardless of size or method of measurement (radians or degrees). 

The value of an angle is given as 31 °. Find the measure of the angle in radians. Find the smallest and largest values that its sine and cosine might have and specify the sine and cosine to the appropriate number of digits. 

Fig. 13. DSCscanofcn>sslinedpolystyrene(0.4%diviny]be]izene),identifyingand )/. 6 is the angle, measured in radians of are per mg of samjde, between the extrapol d lines from below 7 and above 7jj whose intersection is defined as Tui is the corresponding angle at Tw Heating rate, 40 K/min.

At being the change in angle (measured in radians), the bending force constant (in kcal/mole). The Ki and values are determined by IR spectroscopy. 

Series for the Trigonometric Functions. In the following formulas, all angles must be expressed in radians. If D = the number of degrees in the angle, and x = its radian measure, then x = 0.017453Z7. 

Models for description of liquids should provide us with an understanding of the dynamic behavior of the molecules, and thus of the routes of chemical reactions in the liquids. While it is often relatively easy to describe the molecular structure and dynamics of the gaseous or the solid state, this is not true for the liquid state. Molecules in liquids can perform vibrations, rotations, and translations. A successful model often used for the description of molecular rotational processes in liquids is the rotational diffusion model, in which it is assumed that the molecules rotate by small angular steps about the molecular rotation axes. One quantity to describe the rotational speed of molecules is the reorientational correlation time T, which is a measure for the average time elapsed when a molecule has rotated through an angle of the order of 1 radian, or approximately 60°. It is indirectly proportional to the velocity of rotational motion. 

Directed Angles 27. Basic Trigonometric Functions 28. Radian Measure 28. Trigonometric Properties 29. Hyperbolic Functions 33. Polar Coordinate System 34. 

The value L/r is the radian measure of the arc and therefore of its central angle 0, so that... 

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