The arcs in the photo at the right appear to be paths of stars rotating about the North Star. To produce this effect, the photographer set a camera on a tripod and left the shutter open for an extended time. If the photographer left the shutter open for a full 24 hours, each arc would be a complete circle.
You can model a star’s “rotation” in the coordinate plane. Place the North Star at the origin. Let P(1, 0) be the position of the star at the moment the camera’s shutter opens. Suppose the shutter is left open for 2 h 40 min, with the arc ending at P`.
a. What angle of rotation maps P onto

Question

The arcs in the photo at the right appear to be paths of stars rotating about the North Star. To produce this effect, the photographer set a camera on a tripod and left the shutter open for an extended time. If the photographer left the shutter open for a full 24 hours, each arc would be a complete circle.
You can model a star’s “rotation” in the coordinate plane. Place the North Star at the origin. Let P(1, 0) be the position of the star at the moment the camera’s shutter opens. Suppose the shutter is left open for 2 h 40 min, with the arc ending at P`.
a. What angle of rotation maps P onto