public static void Cos(PlotControl plot)
{
// We create a new CosFunction, set its parameters and add it to the
// PlotModel plot.
CosFunction cos = new CosFunction();
cos.Color = Color.Red;
cos.LineWidth = 2;
cos.LineStyle = DashStyle.Dash;
plot.Model.Add(cos);
}
/// <summary>
///
/// </summary>
/// <param name="sf">sin function</param>
/// <param name="cf">cos function</param>
/// <param name="sp">sin power</param>
/// <param name="cp">cos power</param>
/// <returns></returns>
private static ExComp SinCosTrig(SinFunction sf, CosFunction cf, int sp, int cp, string dispStr, AlgebraComp dVar, ref EvalData pEvalData)
{
if (!sf.GetInnerEx().IsEqualTo(cf.GetInnerEx()))
return null;
bool spEven = sp % 2 == 0;
bool cpEven = cp % 2 == 0;
if (spEven && !cpEven)
{
// Use cos^2(x) = 1 - sin^2(x)
ExComp subbedCos = PowOp.StaticCombine(
SubOp.StaticCombine(
ExNumber.GetOne(),
PowOp.StaticCombine(new SinFunction(cf.GetInnerEx()), new ExNumber(2.0))),
new ExNumber((cp - 1) / 2));
subbedCos = MulOp.StaticCombine(cf, MulOp.StaticCombine(PowOp.StaticCombine(sf, new ExNumber(sp)), subbedCos));
pEvalData.GetWorkMgr().FromFormatted(WorkMgr.STM + dispStr + " = \\int ( " + WorkMgr.ToDisp(subbedCos) + " ) d" + dVar.ToDispString() + WorkMgr.EDM,
"Use the identity " + WorkMgr.STM + "cos^{2}(x)=1-sin^{2}(x)" + WorkMgr.EDM);
return subbedCos;
}
else if (!spEven && cpEven)
{
// Using sin^2(x) = 1 - cos^2(x)
ExComp subbedCos = PowOp.StaticCombine(
SubOp.StaticCombine(
ExNumber.GetOne(),
PowOp.StaticCombine(new CosFunction(sf.GetInnerEx()), new ExNumber(2.0))),
new ExNumber((sp - 1) / 2));
subbedCos = MulOp.StaticCombine(sf, MulOp.StaticCombine(PowOp.StaticCombine(cf, new ExNumber(cp)), subbedCos));
pEvalData.GetWorkMgr().FromFormatted(WorkMgr.STM + dispStr + " = \\int ( " + WorkMgr.ToDisp(subbedCos) + " ) d" + dVar.ToDispString() + WorkMgr.EDM,
"Use the identity " + WorkMgr.STM + "sin^{2}(x)=1-cos^{2}(x)" + WorkMgr.EDM);
return subbedCos;
}
else if (spEven && cpEven)
{
// Using sin^2(x) = (1/2)(1-cos(2x))
// Using cos^2(x) = (1/2)(1+cos(2x))
ExComp sinSub = MulOp.StaticCombine(
AlgebraTerm.FromFraction(ExNumber.GetOne(), new ExNumber(2.0)),
SubOp.StaticCombine(ExNumber.GetOne(), new CosFunction(MulOp.StaticCombine(new ExNumber(2.0), sf.GetInnerEx()))));
ExComp cosSub = MulOp.StaticCombine(
AlgebraTerm.FromFraction(ExNumber.GetOne(), new ExNumber(2.0)),
AddOp.StaticCombine(ExNumber.GetOne(), new CosFunction(MulOp.StaticCombine(new ExNumber(2.0), sf.GetInnerEx()))));
ExComp finalEx = MulOp.StaticCombine(
PowOp.StaticCombine(sinSub, new ExNumber(sp / 2)),
PowOp.StaticCombine(cosSub, new ExNumber(cp / 2)));
pEvalData.GetWorkMgr().FromFormatted(WorkMgr.STM + dispStr + "=" + WorkMgr.ToDisp(finalEx) + WorkMgr.EDM,
"Use the identities " + WorkMgr.STM + "sin^2(x)=\\frac{1}{2}(1-cos(2x))" + WorkMgr.EDM + " and " + WorkMgr.STM +
"cos^2(x)=\\frac{1}{2}(1+cos(2x))" + WorkMgr.EDM);
return finalEx;
}
return null;
}
protected override Function ComputeDerivative(Variable variable)
{
if (cos == null)
{
cos = new CosFunction(f, this);
}
return cos * f.Derivative(variable);
}
public SinFunction(Function f, CosFunction cos)
{
this.f = f;
this.cos = cos;
}
