Answer
Let $t$ be the radian measure of an angle. The arc length is equal to $t~r$. When the radius is $r=1$, then the arc length is equal to $t$.
Work Step by Step
Let $t$ be the radian measure of an angle. One full rotation is $2\pi$ radians. The angle $t$ is a ratio of $\frac{t}{2\pi}$ of one full rotation.
Let $r$ be the radius of the circle. One full rotation around the circle is the circumference of a circle which has an arc length of $2\pi~r$. When the ratio of one full rotation is $\frac{t}{2\pi}$, the arc length is $\frac{t}{2\pi}\times 2\pi~r$ which is equal to $t~r$. When the radius is $r=1$, then the arc length is equal to $t$.
