a full turn every seconds, and is pointing straight up at time . The phase is then the angle from the 12:00 position to the current position of the hand, at time , measured clockwise. The phase concept is most useful when the origin is chosen based on features of . For example, for a sinusoid, a convenient choice is any where the function's value changes from zero to positive. The formula above gives the phase as an angle in radians between 0 and . To get the phase as an angle between and , one uses instead The phase expressed in degrees (from 0° to 360°, or from −180° to +180°) is defined the same way, except with "360°" in place of "2π". Consequences With any of the above definitions, the phase of a periodic signal is periodic too, with the same period : for all . The phase is zero at the start of each period; that is for any integer . Moreover, for any given choice of the origin , the value of the signal for any argument depends only on its phase at . Namely, one can write , where is a function of an angle, defined only for a single full turn, that describes the variation of as ranges over a single period. In fact, every periodic signal with a specific waveform can be expressed as where is a "canonical" function of a phase angle in 0 to 2π, that describes just one cycle of that waveform; and is a scaling factor for the amplitude. (This claim assumes that the starting time chosen to compute the phase of corresponds to argument 0 of .) Adding and comparing phases Since phases are angles, any whole full turns should usually be ignored when performing arithmetic operations on them. That is, the sum and difference of two phases (in degrees) should be computed by the formulas and respectively. Thus, for example, the sum of phase angles is 30° (, minus one full turn), and subtracting 50° from 30° gives a phase of 340° (, plus one full turn). Similar formulas hold for radians, with instead of 360. Phase shift The difference between the phases of two periodic signals and is called the phase difference or phase shift of relative to . At values of when the difference is zero, the two signals are said to be in phase,