Sines Without Right Triangles

(A new question of the week) A recent question dealt with an apparent conflict between the right-triangle definition of sines and cosines, and the unit-circle definition, pertaining to multiples of 90° (angles on the axes). This provides an opportunity to look closely at the relationship between those two definitions. Two definitions Recall that the right-triangle …

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Distances on Earth 3: Planar Approximation

We’ve looked at two formulas for the distance between points given their latitude and longitude; here we’ll examine one more formula, which is valid only for small distances. This is a “flat-earth approximation” to distance.