Degrees Minutes and Seconds
Not all angles will be special angles, or even whole number values. Decimal degrees express angles as a decimal number (like 42.75°), while DMS form (degrees, minutes, seconds) breaks angles into whole degrees, minutes, and seconds (like 42° 45′ 0″).
DMS form (degrees, minutes, seconds)
DMS is a notation used to express decimal valued angles.
- One degree equals 60 minutes and
- One minute equals 60 seconds.
Angles in this form are represented as D° M’ S”.
Converting from Decimal Degrees to DMS Form
When converting from decimal degrees to DMS form, we separate the whole number part (degrees) from the decimal part, then convert the decimal portion into minutes and seconds.
Convert [latex]47.58°[/latex] to DMS form.
How To: Converting Decimal Degrees to DMS
- The whole number part is the degrees
- Multiply the decimal part by 60 to get minutes
- If the minutes have a decimal part, multiply that decimal by 60 to get seconds
- Write your answer in DMS notation: degrees° minutes’ seconds”
Converting from DMS Form to Decimal Degrees
To convert from DMS form to decimal degrees, we work backwards by converting minutes and seconds into decimal fractions of a degree.
How To: Converting DMS to Decimal Degrees
- Start with the degrees as your base number
- Divide the minutes by 60 and add to the degrees
- Divide the seconds by 3600 (since 60 × 60 = 3600) and add to the result
- Write your answer with appropriate decimal places
Using a Calculator for DMS Conversions
Most scientific and graphing calculators have built-in functions to convert between decimal degrees and DMS form.
For TI-84 Calculators:
Converting Decimal to DMS:
- Enter the decimal degree value
- Press [latex]\boxed{\text{2nd}}[/latex] then [latex]\boxed{\text{APPS}}[/latex] (ANGLE menu)
- Select option 4: [latex]\boxed{\text{►DMS}}[/latex]
- Press [latex]\boxed{\text{ENTER}}[/latex]
For example, entering [latex]47.58[/latex] and using [latex]\boxed{\text{►DMS}}[/latex] displays [latex]47° 34' 48"[/latex]
Converting DMS to Decimal:
- Enter the degrees
- Press [latex]\boxed{\text{2nd}}[/latex] then [latex]\boxed{\text{APPS}}[/latex] (ANGLE menu)
- Select option 1: [latex]\boxed{°}[/latex]
- Enter the minutes
- Press [latex]\boxed{\text{2nd}}[/latex] then [latex]\boxed{\text{APPS}}[/latex] (ANGLE menu)
- Select option 2: [latex]\boxed{'}[/latex]
- Enter the seconds
- Press [latex]\boxed{\text{2nd}}[/latex] then [latex]\boxed{\text{APPS}}[/latex] (ANGLE menu)
- Select option 3: [latex]\boxed{"}[/latex]
- Press [latex]\boxed{\text{ENTER}}[/latex]
Converting Radians to DMS Form
Sometimes you need to convert an angle given in radians to DMS form. This requires a two-step process: first convert radians to decimal degrees, then convert decimal degrees to DMS form.