In Exercises 65-70 , use the angle-conversion capabilities...

In Exercises $65-70$ , use the angle-conversion capabilities of a graphing utility to convert the angle measure to $\mathbf{D}^{\circ} \mathbf{M}^{\prime} \mathbf{S}^{\prime \prime}$ form.
$$
-115.8^{\circ}
$$

Key Concepts

Graphing Utility Angle Conversion

Modern graphing utilities and calculators often come equipped with built-in functions to convert between different angle representations. Using these features can simplify the process by automating the conversion from decimal degrees to DMS format, which is helpful for checking work or handling complex calculations efficiently.

Handling Negative Angles in Conversions

When converting negative angles from decimal degrees to DMS format, it is important to maintain the negative sign with the degrees component while the minutes and seconds remain positive. This ensures the angular direction is clearly indicated, as the negative number represents rotation in the opposite direction to that defined as positive.

Angle Measurement Systems

Angles can be expressed in different systems, with the most common being decimal degrees and the degrees, minutes, seconds (DMS) format. Decimal degrees offer a straightforward numerical representation while DMS breaks the angle down into whole degrees, minutes (1/60th of a degree), and seconds (1/3600th of a degree), which is particularly useful in fields such as navigation and astronomy.

Decimal Degree to DMS Conversion

Converting a decimal degree measurement to DMS involves isolating the whole degree component and then converting the fractional part into minutes and seconds. This is done by multiplying the fractional part of the degree by 60 to get minutes, and then taking the fractional part of the minutes and multiplying it by 60 to obtain seconds. This method preserves the accuracy of the measurement in a more detailed representation.

Please give Ace some feedback