Does the following function have a name?
$$\operatorname{boxySine}(t,x) = \begin{cases} \frac{\sin(tx)}{\sin(x)} & x \neq 0 \\ t & \text{otherwise} \end{cases} $$
It appears in describing the position of a point on a circular segment in terms of a position on the chord. For a circular segment of central angle $\theta$ and chord length $c$ the arc (or line segment if $\theta = 0$) can be described in terms of $\operatorname{boxySine}$ as $$ t \in [-1,1] $$ $$ \alpha = \frac{\theta}{2} $$ $$ x = \frac{c}{2}\cdot\operatorname{boxySine}\left(t,\alpha\right) $$ $$ y= -c\cdot\sin\left(\alpha\right)\left(\left(\operatorname{boxySine}\left(\frac{t}{2},\alpha\right)\cdot\cos\left(\frac{\alpha}{2}\right)\right)^{2}-\left(\cos\left(\frac{\alpha t}{2}\right)\cdot \operatorname{boxySine}\left(\frac{1}{2},\alpha\right)\right)^{2}\right) $$
An alternative way to parameterize a circular arc or line segment without using $\operatorname{boxySine}$ would also be an appropriate answer, as it would explain why it might not have a name.
Desmos graph demonstrating that parameterization of an arc
I called it $\operatorname{boxySine}$ because for small values of $t$ the graph of it looks boxy.