trigonometry-equations
Version:
Trigonometry rules to solve equations for angles and sides
242 lines (205 loc) • 25.9 kB
JavaScript
;
Object.defineProperty(exports, "__esModule", {
value: true
});
var _extends = Object.assign || function (target) { for (var i = 1; i < arguments.length; i++) { var source = arguments[i]; for (var key in source) { if (Object.prototype.hasOwnProperty.call(source, key)) { target[key] = source[key]; } } } return target; };
exports.cosineRule = cosineRule;
exports.sineRule = sineRule;
exports.angleRule = angleRule;
exports.ambiguousCaseRule = ambiguousCaseRule;
var _degreesRadians = require('degrees-radians');
var _degreesRadians2 = _interopRequireDefault(_degreesRadians);
var _radiansDegrees = require('radians-degrees');
var _radiansDegrees2 = _interopRequireDefault(_radiansDegrees);
function _interopRequireDefault(obj) { return obj && obj.__esModule ? obj : { default: obj }; }
function _defineProperty(obj, key, value) { if (key in obj) { Object.defineProperty(obj, key, { value: value, enumerable: true, configurable: true, writable: true }); } else { obj[key] = value; } return obj; }
/**
* Uses the law of cosines to solve a partially complete triangle
* @param {object} angles - angle indices and numerical values
* @param {object} sides - side indices and numerical values
* @param {object} findAngle - angle to calculate when there are three sides
* @return {object} error key with the issue description as the value
* @return {object} input with additional key-values pairs of solutions
*/
function cosineRule() {
var _ref = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {},
_ref$angles = _ref.angles,
angles = _ref$angles === undefined ? {} : _ref$angles,
_ref$sides = _ref.sides,
sides = _ref$sides === undefined ? {} : _ref$sides,
error = _ref.error;
var _ref2 = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {},
findAngle = _ref2.findAngle;
if (error) {
return { error: error };
}
if (Object.keys(sides).length < 2) {
return { error: 'cosineRule expects at least 2 sides' };
}
var doubleSides = function doubleSides(keys) {
return keys.reduce(function (sum, key) {
return sum * sides[key];
}, 1) * 2;
};
var squareSides = function squareSides(keys) {
return keys.reduce(function (sum, key) {
return sum + Math.pow(sides[key], 2);
}, 0);
};
var result = void 0;
var segment = void 0;
var segmentName = void 0;
var segmentNumber = void 0;
if (Object.keys(sides).length === 3) {
var firstAngle = [0, 1, 2].findIndex(function (e) {
return !(e in angles);
});
var angle = findAngle || firstAngle;
var twoSides = [0, 1, 2].filter(function (e) {
return e !== Number(angle);
});
var lastSide = Math.pow(sides[angle], 2);
var firstSides = squareSides(twoSides);
result = (0, _radiansDegrees2.default)(Math.acos((firstSides - lastSide) / doubleSides(twoSides)));
segment = angles;
segmentName = 'angles';
segmentNumber = Number(angle);
} else if (Object.keys(sides).length === 2 && Object.keys(angles).length === 1) {
var angleNumber = Object.keys(angles);
var knownAngle = angles[angleNumber];
var knownSides = Object.keys(sides);
var partialResult = doubleSides(knownSides) * Math.cos((0, _degreesRadians2.default)(knownAngle));
result = Math.sqrt(squareSides(knownSides) - partialResult);
segment = sides;
segmentName = 'sides';
segmentNumber = angleNumber;
} else {
return { error: 'cosineRule expected 3 sides or 2 sides and 1 angle' };
}
var resultPair = _defineProperty({}, segmentNumber, result);
var solvedSegment = _defineProperty({}, segmentName, _extends({}, segment, resultPair));
return _extends({ angles: angles, sides: sides }, solvedSegment);
}
/**
* Uses the law of sines to solve a partially complete triangle
* @param {object} angles - angle indices and numerical values
* @param {object} sides - side indices and numerical values
* @return {object} error key with the issue description as the value
* @return {object} input with additional key-values pairs of solutions
*/
function sineRule() {
var _ref3 = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {},
_ref3$angles = _ref3.angles,
angles = _ref3$angles === undefined ? {} : _ref3$angles,
_ref3$sides = _ref3.sides,
sides = _ref3$sides === undefined ? {} : _ref3$sides,
error = _ref3.error;
if (error) {
return { error: error };
}
var match = function match(e) {
return e in angles && e in sides;
};
var partialMatch = function partialMatch(e) {
return (e in angles || e in sides) && !match(e);
};
var firstNonPair = [0, 1, 2].find(partialMatch);
var firstPair = [0, 1, 2].find(match);
if (firstNonPair === undefined) {
return { error: 'sineRule expected an unpaired angle or side' };
}
var knownAngle = angles[firstPair];
var knownSide = sides[firstPair];
var unPairedAngle = angles[firstNonPair];
var unPairedSide = sides[firstNonPair];
var result = void 0;
var segment = void 0;
var segmentName = void 0;
if (unPairedAngle) {
result = knownSide * Math.sin((0, _degreesRadians2.default)(unPairedAngle)) / Math.sin((0, _degreesRadians2.default)(knownAngle));
segment = sides;
segmentName = 'sides';
} else if (knownAngle !== undefined) {
result = (0, _radiansDegrees2.default)(Math.asin(Math.sin((0, _degreesRadians2.default)(knownAngle)) / knownSide * unPairedSide));
segment = angles;
segmentName = 'angles';
} else {
return { error: 'sineRule expected an unpaired angle or side' };
}
var resultPair = _defineProperty({}, firstNonPair, result);
var solvedSegment = _defineProperty({}, segmentName, _extends({}, segment, resultPair));
return _extends({ angles: angles, sides: sides }, solvedSegment);
}
/**
* Uses the angle sum invariant to solve for the last angle in a triangle
* @param {object} angles - angle indices and numerical values
* @param {object} sides - side indices and numerical values
* @return {object} error key with the issue description as the value
* @return {object} input with additional key-values pairs of solutions
*/
function angleRule() {
var _ref4 = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {},
_ref4$angles = _ref4.angles,
angles = _ref4$angles === undefined ? {} : _ref4$angles,
_ref4$sides = _ref4.sides,
sides = _ref4$sides === undefined ? {} : _ref4$sides,
error = _ref4.error;
if (error) {
return { error: error };
}
if (Object.keys(angles).length !== 2) {
return { error: 'angleRule expects 2 angles' };
}
var knownAngles = Object.keys(angles).map(function (e) {
return Number(e);
});
var unknownAngle = [0, 1, 2].filter(function (e) {
return !knownAngles.includes(e);
});
var unknownValue = 180 - knownAngles.reduce(function (sum, key) {
return sum + angles[key];
}, 0);
var lastAngle = _defineProperty({}, unknownAngle, unknownValue);
var allAngles = { angles: _extends({}, angles, lastAngle) };
return _extends({ sides: sides }, allAngles);
}
/**
* Verifies and solves an alternate solution to the given triangle
* @param {object} angles - angle indices and numerical values
* @param {object} sides - side indices and numerical values
* @return {object} error key with the issue description as the value
* @return {object} input with additional key-values pairs of solutions
*/
function ambiguousCaseRule() {
var _ref5 = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {},
_ref5$angles = _ref5.angles,
angles = _ref5$angles === undefined ? {} : _ref5$angles,
_ref5$sides = _ref5.sides,
sides = _ref5$sides === undefined ? {} : _ref5$sides,
error = _ref5.error;
if (error) {
return { error: error };
}
if (Object.keys(angles).length !== 1 || Object.keys(sides).length !== 2) {
return { error: 'ambiguousCaseRule expects 1 angle and 2 sides' };
}
var angleKey = Object.keys(angles).join();
var paired = angleKey in sides;
var findAngle = paired ? sineRule({ angles: angles, sides: sides }) : { angles: angles, sides: sides };
var solvedAngle = Object.keys(findAngle.angles).find(function (e) {
return !(e in angles);
});
var otherAngle = 180 - findAngle.angles[solvedAngle];
var acuteAngle = angles[angleKey] < 90;
var otherSide = Object.keys(sides).find(function (e) {
return e !== angleKey;
});
var smallSide = sides[angleKey] < sides[otherSide];
var validAngle = otherAngle < 180;
if (!acuteAngle || !paired || !smallSide || !validAngle) return {};
var alternateAngles = _extends({}, angles, _defineProperty({}, solvedAngle, otherAngle));
var alternate = _extends({ angles: alternateAngles }, { sides: sides });
var ambiguous = sineRule(angleRule(alternate));
return { ambiguous: ambiguous };
}
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radians from 'degrees-radians'\nimport degrees from 'radians-degrees'\n\n/**\n* Uses the law of cosines to solve a partially complete triangle\n* @param {object} angles - angle indices and numerical values\n* @param {object} sides - side indices and numerical values\n* @param {object} findAngle - angle to calculate when there are three sides\n* @return {object} error key with the issue description as the value\n* @return {object} input with additional key-values pairs of solutions\n*/\nexport function cosineRule ({ angles = {}, sides = {}, error } = {}, { findAngle } = {}) {\n  if (error) {\n    return { error }\n  }\n\n  if (Object.keys(sides).length < 2) {\n    return { error: 'cosineRule expects at least 2 sides' }\n  }\n\n  const doubleSides = keys => keys.reduce((sum, key) => sum * sides[key], 1) * 2\n  const squareSides = keys => keys.reduce((sum, key) => sum + sides[key] ** 2, 0)\n  let result\n  let segment\n  let segmentName\n  let segmentNumber\n\n  if (Object.keys(sides).length === 3) {\n    const firstAngle = [0, 1, 2].findIndex(e => !(e in angles))\n    const angle = findAngle || firstAngle\n    const twoSides = [0, 1, 2].filter(e => e !== Number(angle))\n    const lastSide = sides[angle] ** 2\n    const firstSides = squareSides(twoSides)\n    result = degrees(Math.acos((firstSides - lastSide) / doubleSides(twoSides)))\n    segment = angles\n    segmentName = 'angles'\n    segmentNumber = Number(angle)\n  } else if (Object.keys(sides).length === 2 && Object.keys(angles).length === 1) {\n    const angleNumber = Object.keys(angles)\n    const knownAngle = angles[angleNumber]\n    const knownSides = Object.keys(sides)\n    const partialResult = doubleSides(knownSides) * Math.cos(radians(knownAngle))\n    result = Math.sqrt(squareSides(knownSides) - partialResult)\n    segment = sides\n    segmentName = 'sides'\n    segmentNumber = angleNumber\n  } else {\n    return { error: 'cosineRule expected 3 sides or 2 sides and 1 angle' }\n  }\n\n  const resultPair = { [segmentNumber]: result }\n  const solvedSegment = { [segmentName]: { ...segment, ...resultPair } }\n\n  return { ...{ angles, sides }, ...solvedSegment }\n}\n\n/**\n* Uses the law of sines to solve a partially complete triangle\n* @param {object} angles - angle indices and numerical values\n* @param {object} sides - side indices and numerical values\n* @return {object} error key with the issue description as the value\n* @return {object} input with additional key-values pairs of solutions\n*/\nexport function sineRule ({ angles = {}, sides = {}, error } = {}) {\n  if (error) {\n    return { error }\n  }\n\n  const match = e => e in angles && e in sides\n  const partialMatch = e => (e in angles || e in sides) && !match(e)\n  const firstNonPair = [0, 1, 2].find(partialMatch)\n  const firstPair = [0, 1, 2].find(match)\n\n  if (firstNonPair === undefined) {\n    return { error: 'sineRule expected an unpaired angle or side' }\n  }\n\n  const knownAngle = angles[firstPair]\n  const knownSide = sides[firstPair]\n  const unPairedAngle = angles[firstNonPair]\n  const unPairedSide = sides[firstNonPair]\n  let result\n  let segment\n  let segmentName\n\n  if (unPairedAngle) {\n    result = knownSide * Math.sin(radians(unPairedAngle)) / Math.sin(radians(knownAngle))\n    segment = sides\n    segmentName = 'sides'\n  } else if (knownAngle !== undefined) {\n    result = degrees(Math.asin(Math.sin(radians(knownAngle)) / knownSide * unPairedSide))\n    segment = angles\n    segmentName = 'angles'\n  } else {\n    return { error: 'sineRule expected an unpaired angle or side' }\n  }\n\n  const resultPair = { [firstNonPair]: result }\n  const solvedSegment = { [segmentName]: { ...segment, ...resultPair } }\n\n  return { ...{ angles, sides }, ...solvedSegment }\n}\n\n/**\n* Uses the angle sum invariant to solve for the last angle in a triangle\n* @param {object} angles - angle indices and numerical values\n* @param {object} sides - side indices and numerical values\n* @return {object} error key with the issue description as the value\n* @return {object} input with additional key-values pairs of solutions\n*/\nexport function angleRule ({ angles = {}, sides = {}, error } = {}) {\n  if (error) {\n    return { error }\n  }\n\n  if (Object.keys(angles).length !== 2) {\n    return { error: 'angleRule expects 2 angles' }\n  }\n\n  const knownAngles = Object.keys(angles).map(e => Number(e))\n  const unknownAngle = [0, 1, 2].filter(e => !knownAngles.includes(e))\n  const unknownValue = 180 - knownAngles.reduce((sum, key) => sum + angles[key], 0)\n  const lastAngle = { [unknownAngle]: unknownValue }\n  const allAngles = { angles: { ...angles, ...lastAngle } }\n\n  return { ...{ sides }, ...allAngles }\n}\n\n/**\n* Verifies and solves an alternate solution to the given triangle\n* @param {object} angles - angle indices and numerical values\n* @param {object} sides - side indices and numerical values\n* @return {object} error key with the issue description as the value\n* @return {object} input with additional key-values pairs of solutions\n*/\nexport function ambiguousCaseRule ({ angles = {}, sides = {}, error } = {}) {\n  if (error) {\n    return { error }\n  }\n\n  if (Object.keys(angles).length !== 1 || Object.keys(sides).length !== 2) {\n    return { error: 'ambiguousCaseRule expects 1 angle and 2 sides' }\n  }\n\n  const angleKey = Object.keys(angles).join()\n  const paired = angleKey in sides\n  const findAngle = paired ? sineRule({ angles, sides }) : { angles, sides }\n  const solvedAngle = Object.keys(findAngle.angles).find(e => !(e in angles))\n  const otherAngle = 180 - findAngle.angles[solvedAngle]\n  const acuteAngle = angles[angleKey] < 90\n  const otherSide = Object.keys(sides).find(e => e !== angleKey)\n  const smallSide = sides[angleKey] < sides[otherSide]\n  const validAngle = otherAngle < 180\n\n  if (!acuteAngle || !paired || !smallSide || !validAngle) return {}\n\n  const alternateAngles = { ...angles, ...{ [solvedAngle]: otherAngle } }\n  const alternate = { ...{ angles: alternateAngles }, ...{ sides } }\n  const ambiguous = sineRule(angleRule(alternate))\n\n  return { ambiguous }\n}\n"]}