Find the measure in radians of the least positive angle that is coterminal with 19pi/2
To find the least positive angle coterminal with $19\pi/2,$ we can subtract as many full revolutions as possible to bring the angle into the interval $[0,2\pi).$ Since $2 \pi$ is equal to $4 \cdot \frac{\pi}{2},$ subtracting $4 \cdot \frac{\pi}{2}$ from $\frac{19 \pi}{2}$ leaves an angle that differs by a multiple of $2 \pi$ from $19 \pi/2,$ as shown below.
[asy]
unitsize(1 cm);
int i;
draw((-3.5,-2.5)--(-2.5,-2.5)--(2.5,2.5)--(3.5,2.5),red);
draw((-2.5,-2.5)--(-3.5,-2.5),red);
draw((2.5,2.5)--(3.5,2.5),red);
draw(Circle((0,0),2),red);
draw((-2.5,0)--(2.5,0),red);
draw((0,-2.5)--(0,2.5),red);
dot("$\frac{19 \pi}{2}$", dir(19*pi/2), N);
dot("$\frac{11 \pi}{2}$", dir(11*pi/2), S);
dot("$\frac{3 \pi}{2}$", dir(3*pi/2), S);
dot("$-\frac{5 \pi}{2}$", dir(-5*pi/2), S);
for (i = -2; i <= 6; ++i) {
draw(dir(i*pi/2)--2*dir(i*pi/2));
}
label("$\dots$", (0,-1.5), red);
label("$\dots$", (0,1.5), red);
label("$\dots$", (-1.5,0), red);
label("$\dots$", (1.5,0), red);
[/asy]
Therefore,
\[\frac{19 \pi}{2} - 4 \cdot \frac{\pi}{2} = \frac{3 \pi}{2}.\]To express the answer in radians, we write $\boxed{\frac{3 \pi}{2}}.$