= longitude difference/increased latitude differenceĬ. This simple file provides the following information (navigation data) : course, distances in nautical miles (great circle and rhumb line), initial course and vertex latitudeĬoordinates must be entered : latitudes and longitudes (degrees- minutes-seconds) "n" for north latitude, "s" for south latitude, "w" for west longitude, "e" for east longitude.įormula : ( 7915,7 * log tan (45° + lat/2)) - (3437,7 * e*e * sine lat)įormula : tang. Files include translations in languages (English, German, Dutch, Spanish and Italian).Ģnd file - Great Circle Sailing - Rhumb Line - (small program) It's essential to enable macros before using the program (calculations are not performed without activating the macro, however, see the instructions in the file). The sheet "Chart1" shows a diagram with the location of some parameters: great circle navigation, rhumb lines, courses, waypoints: The program allows the user to customize all navigation data 60 waypoints (great circle navigation) and 60 rhumb lines can be managed. This feature distinguishes the file from many others currently on the web. It is a logical evolution and completion of the second file. This file is created thanks to the remarkable ability of Jelle Schaap in the development of excel programs. (estimated time of arrival), compass direction, manual-automatic waypoints calculator and planning routes. ) : courses, distances (rhumb line & great circle sailing), orthodromic data ( vertex coordinates ), E.T.A.
#Circl equation maker full version
Great circle sailing (orthodromy) or rhumb line (loxodromic route) ? 1st file - a full version of Great Circle Sailing - Rhumb Line - Waypoints ( full track ) - Route GraphĪ full program for all users (students, sailors, officers and masters of the "merchant navy ".
#Circl equation maker how to
Table showing angles and resulting trig function values.Great circle sailing - nautical calculator of routes and distances great circle navigation and rhumb line - how to calculate distance and course (bearing) between two points - marine great circle formulas - navigation calculatorįormulas, programs and calculations to obtain distance and course (bearing) - loxodromic distances (rhumb line) and orthodromic waypoints (great circle sailing) - orthodromic and loxodromic navigation calculator - two spreadsheet excel files - (free download and use!)ĭistance and course (bearing) between Vigo and Boston. You’ll notice these coordinates and their negative values repeated for the entire unit circle.
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The following table shows common angles and the resulting values using the trig functions for the top right quadrant of the unit circle. Table showing degree to radian conversions for the unit circle. The following table shows degree to radian conversions for the angles in the unit circle. Try these tricks to memorize the unit circle without needing to remember every coordinate. There are a few tricks you can use to memorize the unit circle. The unit circle might intimidate you, but remembering it might be easier than it might seem at first glance.
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Unit Circle Chart Table Table showing the angles and coordinates in the unit circle chart. The chart shows the angles in radians and degrees, and shows each coordinate solved using the special right triangle created using the unit circle. The unit circle chart shows the angles used in the 30-60-90 and 45-45-90 special right triangles, and the coordinates where the radius intersects the edge of the unit circle. (cos θ, sin θ) Unit Circle Chart with Radians and Degrees Thus, the coordinate where the radius intersects the circle is: The base of the triangle is equal to the cosine of the angle, which becomes the x-coordinate.
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The point, or coordinate, where the radius at the defined angle intersects the circle can also be calculated using trigonometric functions.Īs noted above, the edge of the right triangle formed is equal to the sine of the angle θ this becomes the y-coordinate. How to Find Coordinates on the Unit Circle The edge of the triangle (leg a) is equal to the sine of the angle, while the base of the triangle (leg b) is equal to the cosine. Since the radius of the unit circle is 1, the right triangle’s hypotenuse is equal to 1. The unit circle defines how to solve the parts of a right triangle formed when extending a line for a known angle within the circle.