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Likewise, the phase angle difference of two waves can also be expressed using the radian as the unit. For example, if the phase angle difference of two waves is (n⋅2 π) radians, where n is an integer, they are considered to be in phase, whilst if the phase angle difference of two waves is (n⋅2 π + π) radians, with n an integer, they are ...
Additionally, an angle that is a rational multiple of radians is constructible if and only if, when it is expressed as / radians, where a and b are relatively prime integers, the prime factorization of the denominator, b, is the product of some power of two and any number of distinct Fermat primes (a Fermat prime is a prime number one greater ...
Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same.
For example, radiant intensity can be measured in watts per steradian (W⋅sr −1). The steradian was formerly an SI supplementary unit, but this category was abolished in 1995 and the steradian is now considered an SI derived unit. The name steradian is derived from the Greek στερεός stereos 'solid' + radian.
For example, a microphone's pickup pattern illustrates its proportional response to an incoming sound from a given direction, and these patterns can be represented as polar curves. The curve for a standard cardioid microphone, the most common unidirectional microphone, can be represented as r = 0.5 + 0.5sin( ϕ ) at its target design frequency ...
Example ballistic table for a given 7.62×51mm NATO load. Bullet drop and wind drift are shown both in mrad and moa . Milliradian adjustment is commonly used as a unit for clicks in the mechanical adjustment knobs (turrets) of iron and scope sights both in the military and civilian shooting sports .
For example, when =, we get the measure in radians, and the usual trigonometric functions. When a = 360 {\displaystyle a=360} , we get the sine and cosine of angles measured in degrees. Note that a = 2 π {\displaystyle a=2\pi } is the unique value at which the derivative d d t e ( t / a ) {\displaystyle {\frac {d}{dt}}e(t/a)} becomes a unit ...
A small object nearby may subtend the same solid angle as a larger object farther away. For example, although the Moon is much smaller than the Sun, it is also much closer to Earth. Indeed, as viewed from any point on Earth, both objects have approximately the same solid angle (and therefore apparent size). This is evident during a solar eclipse.