Chapter 11 Mathematica Commands

1. Sin Cos Tan

Sin["Degree"°]//N

Cos["Degree"°]//N

Tan["Degree"°]//N

Sin[45°]//N

2. Sin Cos Tan with Degree Minute Second

Sin["Degree"°+"Minute"/60°+"Second"/3600°]//N

Sin["Degree"°+"Minute"/60°+"Second"/3600°]//N

Sin["Degree"°+"Minute"/60°+2"Second"/3600°]//N

Sin[23°+58/60°+21/3600°]//N

3. Inverse Sin Cos Tan to Degrees

N[ArcSin["Expr"]/Degree]

N[ArcCos["Expr"]/Degree]

N[ArcTan["Expr"]/Degree]

N[ArcSin[0.9047]/Degree]

4. SOH CAH TOA

Solve[Sin["Degree"°]==(("Opposite")/("Hypotenuse"))]//N

Solve[Cos["Degree"°]==(("Adjacent")/("Hypotenuse"))]//N

Solve[Tan["Degree"°]==(("Opposite")/("Adjacent"))]//N

5. HERONS FORMULA (Area of a Triangle when you know all three side-lengths)

s:=("first side length"+"second side length"+"third side length")/2//N
Solve[Area==(Sqrt[s(s-"first side length")*(s-"second side length")*(s-"third side length")])]//N

6. Area of a Triangle when you know two side-lengths and one angle

Solve[Area==(1/2)*"first side length"*"second side length"*Sin["Degree"°]]//N

7. Sine Rules

Solve[(("a")/(Sin["A"°]))==(("b")/(Sin["B"°]))]//N

Solve[(("b")/(Sin["B"°]))==(("c")/(Sin["C"°]))]//N

Solve[(("a")/(Sin["A"°]))==(("c")/(Sin["C"°]))]//N

8. Cosine Rules

Solve[(("a")^2)==(("b")^2)+(("c")^2)-2*"b"*"c"*Cos["A"°]]//N

Solve[(("b")^2)==(("a")^2)+(("c")^2)-2*"a"*"c"*Cos["B"°]]//N

Solve[(("c")^2)==(("a")^2)+(("b")^2)-2*"a"*"b"*Cos["C"°]]//N