Question

1. use the arc length formula to find r if s = 14 and θ = 42°.

a) \\(\frac{60}{π}\\)

b) \\(\frac{30}{π}\\)

c) \\(\frac{120}{π}\\)

d) \\(\frac{1}{3}\\)

Explanation:

Step1: Convert degrees to radians

$\theta = 42^\circ = 42 \times \frac{\pi}{180} = \frac{7\pi}{30}$

Step2: Rearrange arc length formula

The arc length formula is $s = r\theta$, solve for $r$: $r = \frac{s}{\theta}$

Step3: Substitute values and simplify

$r = \frac{14}{\frac{7\pi}{30}} = 14 \times \frac{30}{7\pi} = \frac{60}{\pi}$

Answer:

a) $\boldsymbol{\frac{60}{\pi}}$