Let (x1,y1) and (x2,y2) be points on the unit circle corresponding to t=t1 and t= pi - t1, respectively.?

Question

Explain or identify the symmetry of the points (x1,y1) and (x2,y2)
Explain me a conjeture about any relationship between sin(t1) and cos(t1+pi)
Explain me a conjeture about any relationship between cos(t1) and cos(t1+pi).
please if anybody can do this, i cant understand it.

Answer 1

The points (x1, y1) and (x2, y2) are points of radial symmetry on the unit circle. In other words, both on the same line passing through the origin and on opposite sides of the unit circle. Both the sine and the cosine of t1 and t1 + π are negatives of each other since the sign of any coordinate changes from one quadrant to a point 180 degrees away.