Convert hour angle to half circle

Learn how to convert 1 hour angle to half circle step by step.

Calculation Breakdown

Set up the equation

\(1.0\left(hour \text{ } angle\right)={\color{rgb(20,165,174)} x}\left(half \text{ } circle\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(radian\right)\)

\(\text{Left side: 1.0 } \left(hour \text{ } angle\right) = {\color{rgb(89,182,91)} \dfrac{π}{12.0}\left(radian\right)} = {\color{rgb(89,182,91)} \dfrac{π}{12.0}\left(rad\right)}\)

\(\text{Right side: 1.0 } \left(half \text{ } circle\right) = {\color{rgb(125,164,120)} π\left(radian\right)} = {\color{rgb(125,164,120)} π\left(rad\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(hour \text{ } angle\right)={\color{rgb(20,165,174)} x}\left(half \text{ } circle\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{12.0}} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} π}} \times {\color{rgb(125,164,120)} \left(radian\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{12.0}} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} π} \cdot {\color{rgb(125,164,120)} \left(rad\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{12.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} π} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{π}{12.0} = {\color{rgb(20,165,174)} x} \times π\)

Cancel factors on both sides

\(\text{Cancel factors}\)

\(\dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{12.0} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{π}}\)

\(\text{Simplify}\)

\(\dfrac{1.0}{12.0} = {\color{rgb(20,165,174)} x}\)

Switch sides

\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{12.0}\)

Solve \({\color{rgb(20,165,174)} x}\)

\({\color{rgb(20,165,174)} x}\approx0.0833333333\approx8.3333 \times 10^{-2}\)

\(\text{Conversion Equation}\)