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Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere. Analogous to one degree being equal to π / 180 radians, a square degree is equal to ( π / 180 ) 2 steradians (sr), or about 1 / 3283 sr or about 3.046 × 10 −4 sr.
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A solid angle of one steradian subtends a cone aperture of approximately 1.144 radians or 65.54 degrees. In the SI, solid angle is considered to be a dimensionless quantity, the ratio of the area projected onto a surrounding sphere and the square of the sphere's radius. This is the number of square radians in the solid angle.
The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
Each degree square is designated by a full reference to the main degree square. S01E010 is a reference to a square in Tanzania. S means the square is south of equator, and E means it is East of the zero meridian. The numbers refer to longitudinal and latitudinal degree. A square with no sublevel reference is also called QDGC level 0.
The sign of the square root needs to be chosen properly—note that if 2 π is added to θ, the quantities inside the square roots are unchanged, but the left-hand-sides of the equations change sign. Therefore, the correct sign to use depends on the value of θ.
√ (square-root symbol) Denotes square root and is read as the square root of. Rarely used in modern mathematics without a horizontal bar delimiting the width of its argument (see the next item). For example, √2. √ (radical symbol) 1. Denotes square root and is read as the square root of.
C-squares (acronym for the Concise Spatial QUery And REpresentation System) is a system of spatially unique, location-based identifiers for areas on the surface of the earth, represented as cells from a latitude- and longitude-based Discrete Global Grid at a hierarchical set of resolution steps, obtained by progressively subdividing 10×10 degree World Meteorological Organization squares; the ...