Wolfram Computation Meets Knowledge

Wolfram Formula Repository (Under Development)

Spherical Law of Cosines Using Angles

The spherical law of cosines is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry.

The cosine of the angle opposite the third side equals the product of the cosine of the angular length of the third side and the sines of the angles opposite the first and second sides minus the product of the cosines of the angles opposite the first and second sides.

Formula

Cos[QuantityVariable["γ", "Angle"]] == -(Cos[QuantityVariable["α", "Angle"]]*Cos[QuantityVariable["β", "Angle"]]) + Cos[QuantityVariable["c", "Angle"]]*Sin[QuantityVariable["α", "Angle"]]*Sin[QuantityVariable["β", "Angle"]]

symbol description physical quantity
γ angle opposite third side "Angle"
α angle opposite first side "Angle"
β angle opposite second side "Angle"
c third side angular length "Angle"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Spherical Law of Cosines Using Angles"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Spherical Law of Cosines Using Angles"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Spherical Law of Cosines Using Angles"], {QuantityVariable[ "c","Angle"] -> Quantity[\[Pi]/2, "Radians"], QuantityVariable["\[Gamma]","Angle"] -> Quantity[\[Pi]/2, "Radians"]}]
Out[3]=

Publisher Information