Question

for the key points shown in the four quadrants on the unit circle, identify a significant pattern or symmetry in the angles, the coordinates, the trigonometric functions, or a relationship between them.

Answer 1

Graph 1

From this graph, we see that the points marked on the circle are:

• the central angle of each quadrant (45°, 135°, 225°, 315°),

,

• the angles that are at a distance of 15° from the central angles (30°-60°, 120°-150°, ...),

,

• the angles that divide the circle into quadrants (90°, 180°, 270°, 360°).

Graph 2

We see that the points marked on the circle follow the same pattern as for Graph 1. The change with respect to the previous graph is that we have the cartesian coordinates of the points instead of the polar coordinates given by an angle.