檢視三角函數有理化的原始碼

[[分類:數學]]<!-- 程式在：jendo.org/study/三角函數有理化.php -->
<div style='float:right'><img src='http://jendo.org/uploadFiles/學習資源/數學/0-90deg3digitsTangentValues.jpg' width=380 height=*/><br/><img src='http://jendo.org/uploadFiles/學習資源/數學/0-90deg4digitsTrigonometryValues.jpg' width=380 height=*/></div>
<table class=nicetable>
<tr><th></th><th>90°/1</th><th>90°/1.5</th><th>90°/2</th><th>90°/2.5</th><th>90°/3</th><th>90°/4</th><th>90°/5</th><th>90°/6</th><th>90°/∞</th></tr>
<tr><th>特殊角</th><th>tan90°</th><th>tan60°</th><th>tan45°</th><th>tan36°</th><th>tan30°</th><th>tan22.5°</th><th>tan18°</th><th>tan15°</th><th>tan0°</th></tr>
<tr><th>有理值</th><th>∞</th><th>7/4<br/>71/41</th><th>1</th><th>5/7<br/>73/100<br/>8/11</th><th>4/7<br/>41/71</th><th>5/12<br/>29/70</th><th>13/40</th><th>3/11<br/>15/56</th><th>0</th></tr>
<tr><th>其餘角</th><th></th><th></th><th></th><th>tan54°</th><th></th><th>tan67.5°</th><th>tan72°</th><th>tan75°</th><th></th></tr>
<tr><th>有理值</th><th></th><th></th><th></th><th>7/5<br/>11/8</th><th></th><th>12/5<br/>70/29</th><th>40/13</th><th>11/3<br/>56/15</th><th></th></tr>
<tr><th>其半角</th><th></th><th></th><th></th><th>tan27°</th><th></th><th></th><th>tan9°</th><th></th><th></th></tr>
<tr><th>有理值</th><th></th><th></th><th></th><th>1/2<br/>27/53</th><th></th><th></th><th>4/25<br/>16/101</th><th></th><th></th></tr>
</table>
#tan0° = 0
#tan9° ≅ 3/19 或 4/25 或 16/101(高精)
#tan15° ≅ 3/11 或 15/56(高精)
#tan18° ≅ 13/40(高精)
#tan22.5° ≅ 5/12 或 29/70(高精)
#tan27° ≅ 1/2 或 27/53(高精)
#tan30° ≅ 4/7 或 41/71(高精)
#tan36° ≅ 5/7 或 73/100 或 8/11(高精)
#tan45° = 1
#tan54° ≅ 7/5 或 11/8(高精)
#tan60° ≅ 7/4 或 71/41(高精)
#tan67.5° ≅ 12/5 或 70/29(高精)
#tan72° ≅ 40/13(高精)
#tan75° ≅ 11/3 或 56/15(高精)
#tan90° ≅ ∞
tanθ×tan(90°-θ)=1

tan36.87° 或 tan36.86989° ≅ 3/4

tan46.4° 或 tan46.39718° ≅ 21/20