Question

1 fill in the blank 5 points

1. the formula \\(\frac{\text{deg}}{360}(2\pi r)\\) equals answer .
2. the formula \\(\frac{\text{deg}}{360}(\pi r^2)\\) equals answer .
3. when converting from answer to answer you multiply by \\(\frac{\pi}{180}\\)
4. when converting from answer to answer you multiply by \\(\frac{180}{\pi}\\)

\boxed{radian} \boxed{degree} \boxed{radian} \boxed{sector area} \boxed{arc length} \boxed{arc area} \boxed{sector length}

Explanation:

1.

Step1: Recall arc length formula

The formula for the length of an arc of a circle with radius \( r \) and central angle \( \text{deg} \) degrees is derived from the circumference \( 2\pi r \). The fraction of the circle's circumference corresponding to the central angle \( \text{deg} \) is \( \frac{\text{deg}}{360} \), so multiplying by the circumference gives the arc length.
\(\frac{\text{deg}}{360}(2\pi r)\) is the formula for arc length.

Step2: Identify the term

So the formula \(\frac{\text{deg}}{360}(2\pi r)\) equals arc length.

Step1: Recall sector area formula

The area of a sector of a circle with radius \( r \) and central angle \( \text{deg} \) degrees is a fraction of the circle's area \( \pi r^2 \). The fraction is \( \frac{\text{deg}}{360} \), so multiplying by the circle's area gives the sector area.
\(\frac{\text{deg}}{360}(\pi r^2)\) is the formula for sector area.

Step2: Identify the term

So the formula \(\frac{\text{deg}}{360}(\pi r^2)\) equals sector area.

Step1: Recall angle conversion

To convert from degrees to radians, we use the conversion factor \( \frac{\pi}{180} \). That is, if we have an angle in degrees, we multiply by \( \frac{\pi}{180} \) to get the angle in radians.

Step2: Determine the units

So when converting from degree to radian, we multiply by \( \frac{\pi}{180} \).

Answer:

arc length

2.