Convert half circle to hour angle

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

Calculation Breakdown

Set up the equation

1.0 (h a l f c i r c l e) = x (h o u r a n g l e)

Define the base values of the selected units in relation to the SI unit

(r a d i a n)

Left side: 1.0 (h a l f c i r c l e) = π (r a d i a n) = π (r a d)

Right side: 1.0 (h o u r a n g l e) = \frac{π}{12.0} (r a d i a n) = \frac{π}{12.0} (r a d)

Insert known values into the conversion equation to determine

x

1.0 (h a l f c i r c l e) = x (h o u r a n g l e)

Insert known values =>

1.0 \times π \times (r a d i a n) = x \times \frac{π}{12.0} \times (r a d i a n)

Or

1.0 \cdot π \cdot (r a d) = x \cdot \frac{π}{12.0} \cdot (r a d)

Cancel SI units

1.0 \times π \cdot (r a d) = x \times \frac{π}{12.0} \times (r a d)

Conversion Equation

π = x \times \frac{π}{12.0}

Cancel factors on both sides

Cancel factors

π = x \times \frac{π}{12.0}

Simplify

1.0 = x \times \frac{1.0}{12.0}

Switch sides

x \times \frac{1.0}{12.0} = 1.0

Isolate

x

Multiply both sides by

(\frac{12.0}{1.0})

x \times \frac{1.0}{12.0} \times \frac{12.0}{1.0} = \times \frac{12.0}{1.0}

Cancel

x \times \frac{1.0 \times 12.0}{12.0 \times 1.0} = \frac{12.0}{1.0}

Simplify

x = 12.0

Solve

x

x = 12

Conversion Equation

1.0 (h a l f c i r c l e) = 12 (h o u r a n g l e)

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