∴在角α的终边上任取一点P（4t，-3t）（t≠0），
则x=4t，y=-3t，r=
| x2+y2 |
| (4t)2+(−3t)2 |
当t＞0时，r=5t，
sinα=
| y |
| r |
| −3t |
| 5t |
| 3 |
| 5 |
| x |
| r |
| 4t |
| 5t |
| 4 |
| 5 |
| y |
| x |
| −3t |
| 4t |
| 3 |
| 4 |
当t＜0时，r=-5t，sinα=
| y |
| r |
| −3t |
| −5t |
| 3 |
| 5 |
cosα=
| x |
| r |
| 4t |
| −5t |
| 4 |
| 5 |
| y |
| x |
| −3t |
| 4t |
| 3 |
| 4 |
综上可知，t＞0时，sinα=−
| 3 |
| 5 |
| 4 |
| 5 |
| 3 |
| 4 |
t＜0时，sinα=
| 3 |
| 5 |
| 4 |
| 5 |
| 3 |
| 4 |
| x2+y2 |
| (4t)2+(−3t)2 |
| y |
| r |
| −3t |
| 5t |
| 3 |
| 5 |
| x |
| r |
| 4t |
| 5t |
| 4 |
| 5 |
| y |
| x |
| −3t |
| 4t |
| 3 |
| 4 |
| y |
| r |
| −3t |
| −5t |
| 3 |
| 5 |
| x |
| r |
| 4t |
| −5t |
| 4 |
| 5 |
| y |
| x |
| −3t |
| 4t |
| 3 |
| 4 |
| 3 |
| 5 |
| 4 |
| 5 |
| 3 |
| 4 |
| 3 |
| 5 |
| 4 |
| 5 |
| 3 |
| 4 |