If the code you showed here is the real code it can’t give you any result because you have a lot of bugs there.

I’ll try to fix it assuming you wanna rotate 36 points around the origin.

static void display(void)
{
const float PI = 3.1415; // It'll be needed to convert to radians
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glColor3d(0.0,0.0,1.0);
glPushMatrix();
glTranslatef(0.0,0.0,-5.0);
glRotatef(angle,1.0,0.0,0.0);
glBegin(GL_POINTS); // You must avoid if possible the inclusion of "glBegin" inside a loop
for (int i = 1; i <= 36; i++)
{
//glVertex3f(sin(i),cos(i),0.0); // Error!!! sin() and cos() expect the argument to be in radians not degrees
double radian = i * PI / 180; // You must declare "PI" as a constant
glVertex3f(sin(radian), cos(radian), 0); // In this case you can use glVertex2f instead. But it's ok like this.
}
glEnd(); // It was missing in your code.
glPopMatrix();
angle++;
glutSwapBuffers();
}