Angle to Degrees Minutes and Seconds on Ti 84 Calculator

How to Convert Angles to Degrees Minutes and Seconds on TI-84

The TI-84 calculator can convert decimal degrees to DMS format, but it doesn't have a built-in DMS mode. Here's how to do it manually:

Step 1: Enter the Decimal Degrees

First, enter the angle in decimal degrees. For example, if you have 45.75 degrees:

1. Press the 2ND key and then the MODE key to access the angle unit menu.
2. Select DEG to ensure the calculator is in degrees mode.
3. Enter the decimal degrees: 45.75.

Step 2: Separate Degrees and Decimal Part

Now, separate the degrees from the decimal part:

1. Press STO-> (2ND then STO) to store the value in memory.
2. Enter 45 (the whole degrees) and press ENTER.
3. Subtract the whole degrees from the original value: 45.75 - 45 = 0.75.

Step 3: Convert Decimal to Minutes

Convert the decimal part to minutes:

1. Multiply the decimal by 60: 0.75 × 60 = 45 minutes.
2. Store this value in memory: 45 STO->.

Step 4: Separate Minutes and Decimal Part

Now, separate the minutes from the decimal part:

1. Enter 45 (the whole minutes) and press ENTER.
2. Subtract the whole minutes from the previous value: 45 - 45 = 0.

Step 5: Convert Decimal to Seconds

Convert the remaining decimal to seconds:

1. Multiply the decimal by 60: 0 × 60 = 0 seconds.

Final Result

The angle 45.75° is equivalent to 45°45'0".

Formula Explained

The conversion from decimal degrees to DMS uses the following steps:

For example, converting 36.5°:

1. Degrees: 36
2. Minutes: 0.5 × 60 = 30
3. Seconds: 0 × 60 = 0

Result: 36°30'0"

Worked Examples

Example 1: 12.375°

1. Degrees: 12
2. Minutes: 0.375 × 60 = 22.5
3. Seconds: 0.5 × 60 = 30

Result: 12°22'30"

Example 2: 75.25°

1. Degrees: 75
2. Minutes: 0.25 × 60 = 15
3. Seconds: 0 × 60 = 0

Result: 75°15'0"