The vertex of angle α coincides with the origin, and the starting edge coincides with the non-negative semi-axis of X axis. If the point is

P(2,-1) is at the edge of the terminal, and the value of sin2α is found.

The conditions drawn above explain the specific position of the angle in the rectangular coordinate system. Only when this condition is met can the problem be solved by the definition of trigonometric function.

∫P(2，- 1)，

∴OP=√[2？ +(- 1)? ]=√5,

∴sinα=y/OP=- 1/√5=-√5/5，

cosα=X/OP=2/√5=2√5/5，

∫sin 2α= 2 sinαcosα

=2╳(-√5/5)╳(2√5/5)

=-4/5,

∴ sin2α=-4/5。