91Ó°ÊÓ

When converting an angle from radians to degrees, the key formula to know is \[degrees = radians \times \frac{180}{\pi} \]This formula comes from the fundamental fact that there are \(2\pi\) radians in a full circle, which equals 360 degrees.

• That's why \(\pi\) radians are 180 degrees.
• Thus, dividing 180 by \(\pi\), you get the conversion factor \(\frac{180}{\pi}\).

To see this in action, let's convert \(-2\) radians to degrees using the formula. Substitute \(-2\) into the formula:\[degrees = -2 \times \frac{180}{\pi}\]Performing the calculation, it gives approximately \(-114.5916\) degrees. Adding a precision-based note, we can round this to \(-114.6\) degrees if needed.

The degree measure is a way to express angles, commonly used in day-to-day applications. Each circle is divided into 360 equal parts, meaning one full rotation is 360 degrees. This makes it:- Easy to visualize and - Simple for practical uses, such as navigation or architecture. Understanding angles in degrees helps you think about quarter turns (90 degrees), half turns (180 degrees), and so on. In our exercise, we found that \(-2\) radians are approximately \(-114.6\) degrees, indicating a bit more than a third of a full circle—since one-third of 360 degrees is 120 degrees. When using degrees, always check if you need to provide a more or less precise value, based on context.

Radians are another unit for measuring angles, prevalent in mathematics and engineering due to their natural properties in conjunction with the unit circle. One radian is the angle created when the length of the radius is equal to the arc of the circle. This makes

• One full circle equal to \(2\pi\) radians or \(rac{360}{2\pi} \approx 57.2958\) degrees per radian.

Radians simplify many formulas and calculations in calculus and trigonometry. It's important to become comfortable with both degrees and radians, as they are frequently interchanged.Returning to the given problem, the measure \(-2\) radians indicate an angle that requires converting to degrees for easier interpretation, which gives us \(-114.6\) degrees. Understanding contexts will guide when to use radian or degree measures effectively.