正矢计算器

输入角度或弧度,快速计算对应的正矢值。

正矢计算

结果

什么是正矢函数

正矢函数(Versine function),通常用 \(\text{versin}(\theta)\) 表示,是一种历史悠久的三角函数。在直角三角形中,正矢函数的公式为: \( \text{versin}(\theta) = 1 - \cos(\theta) \) 这表明正矢函数是余弦函数的补量,适合描述余弦偏差或距离的变化。

例如,\(\theta = 60^\circ\) 时: \( \text{versin}(60^\circ) = 1 - \cos(60^\circ) = 1 - 0.5 = 0.5 \)

正矢函数图形

versine graph

正矢函数的图形是正弦波的正向偏移,具有以下特性:

  • 周期性:正矢函数的周期为 \(2\pi\)。
  • 定义域:正矢函数的定义域为所有实数 \(\mathbb{R}\)。
  • 值域:\(\text{versin}(\theta) \in [0, 2]\)。
  • 振幅:最大值为 2,最小值为 0。
  • 波形特性:正矢函数随 \(\theta\) 增加而波动,在 \(0\) 和 \(2\pi\) 处达到最小值(0),在 \(\pi\) 处达到最大值(2)。

正矢函数转换表

角度 弧度 正矢值
00
\(\frac{\pi}{36}\)0.0038053
10°\(\frac{\pi}{18}\)0.01519225
15°\(\frac{\pi}{12}\)0.03407417
20°\(\frac{\pi}{9}\)0.06030738
25°\(\frac{5\pi}{36}\)0.09369221
30°\(\frac{\pi}{6}\)0.1339746
35°\(\frac{7\pi}{36}\)0.18084796
40°\(\frac{2\pi}{9}\)0.23395556
45°\(\frac{\pi}{4}\)0.29289322
50°\(\frac{5\pi}{18}\)0.35721239
55°\(\frac{11\pi}{36}\)0.42642356
60°\(\frac{\pi}{3}\)0.5
65°\(\frac{13\pi}{36}\)0.57738174
70°\(\frac{7\pi}{18}\)0.65797986
75°\(\frac{5\pi}{12}\)0.74118095
80°\(\frac{4\pi}{9}\)0.82635182
85°\(\frac{17\pi}{36}\)0.91284426
90°\(\frac{\pi}{2}\)1
95°\(\frac{19\pi}{36}\)1.08715574
100°\(\frac{5\pi}{9}\)1.17364818
105°\(\frac{7\pi}{12}\)1.25881905
110°\(\frac{11\pi}{18}\)1.34202014
115°\(\frac{23\pi}{36}\)1.42261826
120°\(\frac{2\pi}{3}\)1.5
125°\(\frac{25\pi}{36}\)1.57357644
130°\(\frac{13\pi}{18}\)1.64278761
135°\(\frac{3\pi}{4}\)1.70710678
140°\(\frac{7\pi}{9}\)1.76604444
145°\(\frac{29\pi}{36}\)1.81915204
150°\(\frac{5\pi}{6}\)1.8660254
155°\(\frac{31\pi}{36}\)1.90630779
160°\(\frac{8\pi}{9}\)1.93969262
165°\(\frac{11\pi}{12}\)1.96592583
170°\(\frac{17\pi}{18}\)1.98480775
175°\(\frac{35\pi}{36}\)1.9961947
180°π2
185°\(\frac{37\pi}{36}\)1.9961947
190°\(\frac{19\pi}{18}\)1.98480775
195°\(\frac{13\pi}{12}\)1.96592583
200°\(\frac{10\pi}{9}\)1.93969262
205°\(\frac{41\pi}{36}\)1.90630779
210°\(\frac{7\pi}{6}\)1.8660254
215°\(\frac{43\pi}{36}\)1.81915204
220°\(\frac{11\pi}{9}\)1.76604444
225°\(\frac{5\pi}{4}\)1.70710678
230°\(\frac{23\pi}{18}\)1.64278761
235°\(\frac{47\pi}{36}\)1.57357644
240°\(\frac{4\pi}{3}\)1.5
245°\(\frac{49\pi}{36}\)1.42261826
250°\(\frac{25\pi}{18}\)1.34202014
255°\(\frac{17\pi}{12}\)1.25881905
260°\(\frac{13\pi}{9}\)1.17364818
265°\(\frac{53\pi}{36}\)1.08715574
270°\(\frac{3\pi}{2}\)1
275°\(\frac{55\pi}{36}\)0.91284426
280°\(\frac{14\pi}{9}\)0.82635182
285°\(\frac{19\pi}{12}\)0.74118095
290°\(\frac{29\pi}{18}\)0.65797986
295°\(\frac{59\pi}{36}\)0.57738174
300°\(\frac{5\pi}{3}\)0.5
305°\(\frac{61\pi}{36}\)0.42642356
310°\(\frac{31\pi}{18}\)0.35721239
315°\(\frac{7\pi}{4}\)0.29289322
320°\(\frac{16\pi}{9}\)0.23395556
325°\(\frac{65\pi}{36}\)0.18084796
330°\(\frac{11\pi}{6}\)0.1339746
335°\(\frac{67\pi}{36}\)0.09369221
340°\(\frac{17\pi}{9}\)0.06030738
345°\(\frac{23\pi}{12}\)0.03407417
350°\(\frac{35\pi}{18}\)0.01519225
355°\(\frac{71\pi}{36}\)0.0038053
360°0