public void TestArc3() { var func = MathS.Arccos(2 * x); AssertEqEntity(func.Derive(x).Simplify(), (-2) / MathS.Sqrt(1 + (-4) * MathS.Sqr(x))); }
public void Setup() { exprEasy = x + MathS.Sqr(x) - 3; exprMedium = MathS.Sin(x + MathS.Cos(x)) + MathS.Sqrt(x + MathS.Sqr(x)); exprHard = MathS.Sin(x + MathS.Arcsin(x)) / (MathS.Sqr(x) + MathS.Cos(x)) * MathS.Arccos(x / 1200 + 0.00032 / MathS.Cotan(x + 43)); exprSolvable = MathS.FromString("3arccos(2x + a)3 + 6arccos(2x + a)2 - a3 + 3"); }
[TestMethod] public void ArcTrig() => TestSimplify(@"\arcsin\left(\arccos\left(\arctan\left(\arccot\left(x\right)\right)\right)\right)", MathS.Arcsin(MathS.Arccos(MathS.Arctan(MathS.Arccotan(x)))));
/// <summary> /// Returns a set of possible roots of a function, e. g. /// sin(x) = a => /// x = arcsin(a) + 2 pi n /// x = pi - arcsin(a) + 2 pi n /// </summary> /// <param name="func"></param> /// <param name="value"></param> /// <param name="x"></param> /// <returns></returns> public static Set InvertFunctionEntity(FunctionEntity func, Entity value, Entity x) { Entity a = func.Children[0]; Entity b = func.Children.Count == 2 ? func.Children[1] : null; int arg = func.Children.Count == 2 && func.Children[1].FindSubtree(x) != null ? 1 : 0; var n = Utils.FindNextIndex(func + value, "n"); var res = new Set(); var pi = MathS.pi; Set GetNotNullEntites(Set set) { return(set.FiniteWhere(el => el.entType != Entity.EntType.NUMBER || el.GetValue().IsDefinite())); } switch (func.Name) { // Consider case when sin(sin(x)) where double-mention of n occures case "sinf": { // sin(x) = value => x = arcsin(value) + 2pi * n res.AddRange(GetNotNullEntites(FindInvertExpression(a, MathS.Arcsin(value) + 2 * pi * n, x))); // sin(x) = value => x = pi - arcsin(value) + 2pi * n res.AddRange(GetNotNullEntites(FindInvertExpression(a, pi - MathS.Arcsin(value) + 2 * pi * n, x))); return(res); } case "cosf": { // cos(x) = value => x = arccos(value) + 2pi * n res.AddRange(GetNotNullEntites(FindInvertExpression(a, MathS.Arccos(value) + 2 * pi * n, x))); // cos(x) = value => x = -arccos(value) + 2pi * n res.AddRange(GetNotNullEntites(FindInvertExpression(a, -MathS.Arccos(value) - 2 * pi * n, x))); return(res); } case "tanf": { var inverted = FindInvertExpression(a, MathS.Arctan(value) + pi * n, x); // tan(x) = value => x = arctan(value) + pi * n res.AddRange(GetNotNullEntites(inverted)); return(res); } case "cotanf": { var inverted = FindInvertExpression(a, MathS.Arccotan(value) + pi * n, x); // cotan(x) = value => x = arccotan(value) res.AddRange(GetNotNullEntites(inverted)); return(res); } case "arcsinf": // arcsin(x) = value => x = sin(value) if (EntityInBounds(value, ArcsinFrom, ArcsinTo)) { return(GetNotNullEntites(FindInvertExpression(a, MathS.Sin(value), x))); } else { return(Empty); } case "arccosf": // arccos(x) = value => x = cos(value) if (EntityInBounds(value, ArccosFrom, ArccosTo)) { return(GetNotNullEntites(FindInvertExpression(a, MathS.Cos(value), x))); } else { return(Empty); } case "arctanf": // arctan(x) = value => x = tan(value) return(GetNotNullEntites(FindInvertExpression(a, MathS.Tan(value), x))); case "arccotanf": // arccotan(x) = value => x = cotan(value) return(GetNotNullEntites(FindInvertExpression(a, MathS.Cotan(value), x))); case "logf": if (arg != 0) { // log(x, a) = value => x = a ^ value return(GetNotNullEntites(FindInvertExpression(b, MathS.Pow(a, value), x))); } else { // log(a, x) = value => a = x ^ value => x = a ^ (1 / value) return(GetNotNullEntites(FindInvertExpression(a, MathS.Pow(b, 1 / value), x))); } default: throw new SysException("Unknown function"); } }
public void TestPatt10() { var expr = MathS.Arcsin(x * 3) + MathS.Arccos(x * 1); Assert.IsTrue(expr.Simplify() == MathS.Arccos(x) + MathS.Arcsin(3 * x)); }
public void TestPatt7() { var expr = MathS.Arcsin(x * 3) + MathS.Arccos(x * 3); Assert.IsTrue(expr.Simplify() == 0.5 * MathS.pi); }
public void TestArc3() { var func = MathS.Arccos(2 * x); Assert.Equal((-1) / MathS.Sqrt(1 - MathS.Sqr(2 * x)) * 2, func.Differentiate(x).Simplify()); }
public void TestArc3() { var func = MathS.Arccos(2 * x); Assert.IsTrue(func.Derive(x).Simplify() == (-2) * MathS.Pow(1 + (-4) * MathS.Sqr(x), -0.5)); }