Elementary functions¶
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Sin
(x)¶ trigonometric sine function
Example: In> Sin(1) Out> Sin(1); In> N(Sin(1),20) Out> 0.84147098480789650665; In> Sin(Pi/4) Out> Sqrt(2)/2;
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Cos
(x)¶ trigonometric cosine function
Example: In> Cos(1) Out> Cos(1); In> N(Cos(1),20) Out> 0.5403023058681397174; In> Cos(Pi/4) Out> Sqrt(1/2);
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Tan
(x)¶ trigonometric tangent function
Example: In> Tan(1) Out> Tan(1); In> N(Tan(1),20) Out> 1.5574077246549022305; In> Tan(Pi/4) Out> 1;
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ArcSin
(x)¶ inverse trigonometric function arc-sine
Example: In> ArcSin(1) Out> Pi/2; In> ArcSin(1/3) Out> ArcSin(1/3); In> Sin(ArcSin(1/3)) Out> 1/3; In> x:=N(ArcSin(0.75)) Out> 0.848062; In> N(Sin(x)) Out> 0.7499999477;
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ArcCos
(x)¶ inverse trigonometric function arc-cosine
Example: In> ArcCos(0) Out> Pi/2 In> ArcCos(1/3) Out> ArcCos(1/3) In> Cos(ArcCos(1/3)) Out> 1/3 In> x:=N(ArcCos(0.75)) Out> 0.7227342478 In> N(Cos(x)) Out> 0.75
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ArcTan
(x)¶ inverse trigonometric function arc-tangent
Example: In> ArcTan(1) Out> Pi/4 In> ArcTan(1/3) Out> ArcTan(1/3) In> Tan(ArcTan(1/3)) Out> 1/3 In> x:=N(ArcTan(0.75)) Out> 0.643501108793285592213351264945231378078460693359375 In> N(Tan(x)) Out> 0.75
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Exp
(x)¶ exponential function
Example: In> Exp(0) Out> 1; In> Exp(I*Pi) Out> -1; In> N(Exp(1)) Out> 2.7182818284;
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Ln
(x)¶ natural logarithm
Example: In> Ln(1) Out> 0; In> Ln(Exp(x)) Out> x; In> D(x) Ln(x) Out> 1/x;
See also
Exp()
,Arg()
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Sqrt
(x)¶ square root
Example: In> Sqrt(16) Out> 4; In> Sqrt(15) Out> Sqrt(15); In> N(Sqrt(15)) Out> 3.8729833462; In> Sqrt(4/9) Out> 2/3; In> Sqrt(-1) Out> Complex(0,1);