Answer
$\textbf{a.}$ $\dfrac{3\pi}{4}$
$\textbf{b.}$ $144°$
$\textbf{c.}$ $s=\dfrac{40\pi}{3}\approx41.8879$
Work Step by Step
$\textbf{a.}$ Convert $135°$ to radian measure
To convert degrees to radians, multiply the degrees by $\dfrac{\pi}{180°}$ and simplify:
$135°\Big(\dfrac{\pi}{180°}\Big)=\dfrac{135\pi}{180}=\dfrac{3\pi}{4}$
$\textbf{b.}$ Convert $4\pi/5$ to degree measure
To convert radians to degrees, multiply the radians by $\dfrac{180°}{\pi}$ and simplify:
$\Big(\dfrac{4\pi}{5}\Big)\Big(\dfrac{180°}{\pi}\Big)=\dfrac{4(180°)\pi}{5\pi}=\dfrac{720°}{5}=144°$
$\textbf{c.}$ What is the length of the arc on a circle of radius $10$ associated with an angle of $4\pi/3$ (radians)?
The formula for the arc length is $s=r\theta$, where $r$ is the radius of the circle and $\theta$ is the angle measured in radians.
Both the radius and the angle are known. Substitute them into the formula and evaluate to obtain the arc length:
$s=10\Big(\dfrac{4\pi}{3}\Big)=\dfrac{40\pi}{3}\approx41.8879$
