Can you plese explan part B. and tell me the rule for part C.

Question

Th e arcs in the photo at the right appear to be paths of stars rotating about the North Star. To produce this eff ect, 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 Pr. a. What angle of rotation maps P onto Pr? b. What are the x- and y-coordinates of Pr to the nearest thousandth? c. What translation rule maps P onto P

Answer 1

To answer part a), you need a simple proportion:

If it takes 24 hours to travel 360°, then to find the number of degrees traveled in 2 hrs and 40 min (or 8/3 hours), you use this:

360/24 = x/(8/3)

Once you have that angle, create a right triangle with a 40° angle and an hypotenuse of whatever length you want (the size of the circle is irrelevant here). Then use simple right triangle trigonometry to solve for the two missing legs.

Answer 2

Use trig ratios to find "x" and "y":

cos(40°) = x/1

x = cos(40°) = 0.766

sin(40°) = y/1

y = sin(40°) = 0.643

Answer 3

Where is the photo?