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Angles, units and approximations

Sandy Loynd discusses the angular units of degrees and radians, explains small angle approximations and shows how they are used

Up to A-level physics, you will have measured angles in degrees. You will be aware that there are 360 degrees in a circle, 90 degrees in a right angle and so on. Pilots and sailors amongst others know from navigation that we can divide a degree into 60 minutes and a minute into 60 seconds, giving 3600s per degree, so 1 second is 1°/3600, which I am sure you will agree is a very small angle.

Angles expressed in degrees use the degree symbol (°). An angle of 1°/60 is usually called a minute of arc (to distinguish it from a minute of time), abbreviated to arcmin, and is written as 1arcmin or 1′. Similarly, 1′/60 is a second of arc, written as 1arcsec or 1″.

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Analysing the complexities of waves

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