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The angle is typically measured in degrees from the mark of number 12 clockwise. The time is usually based on a 12-hour clock. A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute.
This concept can be visualized by imagining a clock with a hand that turns at constant speed, making a full turn every seconds, and is pointing straight up at time . The phase φ ( t ) {\displaystyle \varphi (t)} is then the angle from the 12:00 position to the current position of the hand, at time t {\displaystyle t} , measured clockwise .
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
The cosine of the hour angle (cos(h)) is used to calculate the solar zenith angle. At solar noon, h = 0.000 so cos(h) = 1, and before and after solar noon the cos(± h) term = the same value for morning (negative hour angle) or afternoon (positive hour angle), so that the Sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time. [5]
The observer then measures or observes the angle made by the intersection of the line of sight to the longitudinal axis, the dimension of length, of the vessel, using the clock analogy. In this analogy, the observer imagines the vessel located on a horizontal clock face with the front at 12:00.
The United States Naval Observatory states "the Equation of Time is the difference apparent solar time minus mean solar time", i.e. if the sun is ahead of the clock the sign is positive, and if the clock is ahead of the sun the sign is negative. [6] [7] The equation of time is shown in the upper graph above for a period of slightly more than a ...
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A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element. The advantage of a pendulum for timekeeping is that it is an approximate harmonic oscillator : It swings back and forth in a precise time interval dependent on its length, and resists swinging at other rates.