Question

1. change to degrees:

\\(\frac{\pi}{18}\\) radians
\\(45^\circ\\)
\\(55^\circ\\)
\\(35^\circ\\)
\\(10^\circ\\)

1. find the arc length to the nearest hundredth.

a circle with 8-inch radius has a central angle of \\(\frac{\pi}{12}\\)
3.57 inches
2.77 inches
2.09 inches
10.57 inches

Explanation:

Question 2

Step1: Recall radian to degree formula

To convert radians to degrees, we use the formula: \( \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} \)

Step2: Substitute the given radian value

We have \( \frac{\pi}{18} \) radians. Substituting into the formula: \( \frac{\pi}{18} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) cancels out, and \( \frac{180}{18} = 10 \). So we get \( 10^\circ \)

Step1: Recall arc length formula

The formula for arc length \( s \) when the central angle \( \theta \) is in radians is \( s = r\theta \), where \( r \) is the radius.

Step2: Identify given values

Here, \( r = 8 \) inches and \( \theta = \frac{\pi}{12} \) radians.

Step3: Substitute into the formula

\( s = 8\times\frac{\pi}{12} \)

Step4: Simplify and calculate

Simplify \( 8\times\frac{\pi}{12}=\frac{2\pi}{3}\approx\frac{2\times 3.1416}{3}\approx 2.09 \) inches

Answer:

D. \( 10^\circ \)

Question 3