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.
$$
-345.12^{\circ}
$$

Key Concepts

Angle Measurement

Angle measurement involves quantifying the amount of rotation between two intersecting lines and is often expressed in units such as degrees, radians, or revolutions. This concept is foundational in trigonometry and geometry, providing a way to describe the size of an angle in a standardized manner.

Degrees, Minutes, Seconds (DMS) Format

The DMS format breaks down a degree into minutes and seconds, where one degree equals 60 minutes and one minute equals 60 seconds. This expression is particularly useful for providing a more precise representation of an angle, especially in applications that require high levels of accuracy such as navigation and surveying.

Decimal Degree to DMS Conversion

Converting an angle from decimal degree form to the DMS format involves isolating the whole number component for degrees, then multiplying the fractional component by 60 to obtain minutes, and finally converting any remaining fractional minutes to seconds by multiplying by 60. This series of steps is essential for transitioning between the two forms of angle measurement.

Graphing Utility for Angle Conversion

A graphing utility is a tool that can perform complex calculations, including converting between different angle measurements. In the context of angle conversion, it can automate the process of converting a decimal degree measure into its equivalent in the DMS format, thereby reducing manual calculation errors and saving time.

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