用半角公式也可倍角公式推得:cos45=2(cos22.5)²-1=1-2(sin22.5)²,解得sin22.5=[√(2-√2)]/2,cos22.5=[√(2+√2)]/2。
角α | 弧度制 | sinα | cosα | tanα |
0° | o | o | 1 | o |
30° | π/6 | 1/2 | √3/2 | √3/3 |
45° | π/4 | √2/2 | √2/2 | 1 |
60° | π/3 | √3/2 | 1/2 | √3 |
90° | π/2 | 1 | 0 | - |
120° | 2π/3 | √3/2 | -0.5 | -√3 |
135° | 3π/4 | √2/2 | -√2/2 | -1 |
150° | 5π/6 | 1/2 | -√3/2 | -√3/3 |
180° | π | 0 | -1 | 0 |
270° | 3π/2 | -1 | 0 | - |
360° | 2π | 0 | 1 | 0 |