Question

1. give the radian measure of $\theta$ if: a. $r = 5$ and $s = 6$ b. $r = 8$ and $s = 6$

Explanation:

Step1: Recall the arc - length formula

The formula for arc - length is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius of the circle, and $\theta$ is the central angle in radians. We can solve for $\theta$ by the formula $\theta=\frac{s}{r}$.

Step2: Solve part a

Given $r = 5$ and $s = 6$. Substitute these values into the formula $\theta=\frac{s}{r}$. So, $\theta=\frac{6}{5}=1.2$ radians.

Step3: Solve part b

Given $r = 8$ and $s = 6$. Substitute into the formula $\theta=\frac{s}{r}$. So, $\theta=\frac{6}{8}=\frac{3}{4}=0.75$ radians.

Answer:

a. $1.2$ radians
b. $0.75$ radians