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Binary cosinus

Example table for binary cosinus

Note the +/- pattern inside the square-roots.

0.000000 degrees1 = 1.000000...
1.406250 degrees

Click here to show formula
= 0.999699...
2.812500 degrees

Click here to show formula
= 0.998795...
4.218750 degrees

Click here to show formula
= 0.997290...
5.625000 degrees

Click here to show formula
= 0.995185...
7.031250 degrees

Click here to show formula
= 0.992480...
8.437500 degrees

Click here to show formula
= 0.989177...
9.843750 degrees

Click here to show formula
= 0.985278...
11.250000 degrees

Click here to show formula
= 0.980785...
12.656250 degrees

Click here to show formula
= 0.975702...
14.062500 degrees

Click here to show formula
= 0.970031...
15.468750 degrees

Click here to show formula
= 0.963776...
16.875000 degrees

Click here to show formula
= 0.956940...
18.281250 degrees

Click here to show formula
= 0.949528...
19.687500 degrees

Click here to show formula
= 0.941544...
21.093750 degrees

Click here to show formula
= 0.932993...
22.500000 degrees

Click here to show formula
= 0.923880...
23.906250 degrees

Click here to show formula
= 0.914210...
25.312500 degrees

Click here to show formula
= 0.903989...
26.718750 degrees

Click here to show formula
= 0.893224...
28.125000 degrees

Click here to show formula
= 0.881921...
29.531250 degrees

Click here to show formula
= 0.870087...
30.937500 degrees

Click here to show formula
= 0.857729...
32.343750 degrees

Click here to show formula
= 0.844854...
33.750000 degrees

Click here to show formula
= 0.831470...
35.156250 degrees

Click here to show formula
= 0.817585...
36.562500 degrees

Click here to show formula
= 0.803208...
37.968750 degrees

Click here to show formula
= 0.788346...
39.375000 degrees

Click here to show formula
= 0.773010...
40.781250 degrees

Click here to show formula
= 0.757209...
42.187500 degrees

Click here to show formula
= 0.740951...
43.593750 degrees

Click here to show formula
= 0.724247...
45.000000 degrees

Click here to show formula
= 0.707107...
46.406250 degrees

Click here to show formula
= 0.689541...
47.812500 degrees

Click here to show formula
= 0.671559...
49.218750 degrees

Click here to show formula
= 0.653173...
50.625000 degrees

Click here to show formula
= 0.634393...
52.031250 degrees

Click here to show formula
= 0.615232...
53.437500 degrees

Click here to show formula
= 0.595699...
54.843750 degrees

Click here to show formula
= 0.575808...
56.250000 degrees

Click here to show formula
= 0.555570...
57.656250 degrees

Click here to show formula
= 0.534998...
59.062500 degrees

Click here to show formula
= 0.514103...
60.468750 degrees

Click here to show formula
= 0.492898...
61.875000 degrees

Click here to show formula
= 0.471397...
63.281250 degrees

Click here to show formula
= 0.449611...
64.687500 degrees

Click here to show formula
= 0.427555...
66.093750 degrees

Click here to show formula
= 0.405241...
67.500000 degrees

Click here to show formula
= 0.382683...
68.906250 degrees

Click here to show formula
= 0.359895...
70.312500 degrees

Click here to show formula
= 0.336890...
71.718750 degrees

Click here to show formula
= 0.313682...
73.125000 degrees

Click here to show formula
= 0.290285...
74.531250 degrees

Click here to show formula
= 0.266713...
75.937500 degrees

Click here to show formula
= 0.242980...
77.343750 degrees

Click here to show formula
= 0.219101...
78.750000 degrees

Click here to show formula
= 0.195090...
80.156250 degrees

Click here to show formula
= 0.170962...
81.562500 degrees

Click here to show formula
= 0.146730...
82.968750 degrees

Click here to show formula
= 0.122411...
84.375000 degrees

Click here to show formula
= 0.098017...
85.781250 degrees

Click here to show formula
= 0.073565...
87.187500 degrees

Click here to show formula
= 0.049068...
88.593750 degrees

Click here to show formula
= 0.024541...
90.000000 degrees

Click here to show formula
= -0.000000...
91.406250 degrees

Click here to show formula
= -0.024541...
92.812500 degrees

Click here to show formula
= -0.049068...
94.218750 degrees

Click here to show formula
= -0.073565...
95.625000 degrees

Click here to show formula
= -0.098017...
97.031250 degrees

Click here to show formula
= -0.122411...
98.437500 degrees

Click here to show formula
= -0.146730...
99.843750 degrees

Click here to show formula
= -0.170962...
101.250000 degrees

Click here to show formula
= -0.195090...
102.656250 degrees

Click here to show formula
= -0.219101...
104.062500 degrees

Click here to show formula
= -0.242980...
105.468750 degrees

Click here to show formula
= -0.266713...
106.875000 degrees

Click here to show formula
= -0.290285...
108.281250 degrees

Click here to show formula
= -0.313682...
109.687500 degrees

Click here to show formula
= -0.336890...
111.093750 degrees

Click here to show formula
= -0.359895...
112.500000 degrees

Click here to show formula
= -0.382683...
113.906250 degrees

Click here to show formula
= -0.405241...
115.312500 degrees

Click here to show formula
= -0.427555...
116.718750 degrees

Click here to show formula
= -0.449611...
118.125000 degrees

Click here to show formula
= -0.471397...
119.531250 degrees

Click here to show formula
= -0.492898...
120.937500 degrees

Click here to show formula
= -0.514103...
122.343750 degrees

Click here to show formula
= -0.534998...
123.750000 degrees

Click here to show formula
= -0.555570...
125.156250 degrees

Click here to show formula
= -0.575808...
126.562500 degrees

Click here to show formula
= -0.595699...
127.968750 degrees

Click here to show formula
= -0.615232...
129.375000 degrees

Click here to show formula
= -0.634393...
130.781250 degrees

Click here to show formula
= -0.653173...
132.187500 degrees

Click here to show formula
= -0.671559...
133.593750 degrees

Click here to show formula
= -0.689541...
135.000000 degrees

Click here to show formula
= -0.707107...
136.406250 degrees

Click here to show formula
= -0.724247...
137.812500 degrees

Click here to show formula
= -0.740951...
139.218750 degrees

Click here to show formula
= -0.757209...
140.625000 degrees

Click here to show formula
= -0.773010...
142.031250 degrees

Click here to show formula
= -0.788346...
143.437500 degrees

Click here to show formula
= -0.803208...
144.843750 degrees

Click here to show formula
= -0.817585...
146.250000 degrees

Click here to show formula
= -0.831470...
147.656250 degrees

Click here to show formula
= -0.844854...
149.062500 degrees

Click here to show formula
= -0.857729...
150.468750 degrees

Click here to show formula
= -0.870087...
151.875000 degrees

Click here to show formula
= -0.881921...
153.281250 degrees

Click here to show formula
= -0.893224...
154.687500 degrees

Click here to show formula
= -0.903989...
156.093750 degrees

Click here to show formula
= -0.914210...
157.500000 degrees

Click here to show formula
= -0.923880...
158.906250 degrees

Click here to show formula
= -0.932993...
160.312500 degrees

Click here to show formula
= -0.941544...
161.718750 degrees

Click here to show formula
= -0.949528...
163.125000 degrees

Click here to show formula
= -0.956940...
164.531250 degrees

Click here to show formula
= -0.963776...
165.937500 degrees

Click here to show formula
= -0.970031...
167.343750 degrees

Click here to show formula
= -0.975702...
168.750000 degrees

Click here to show formula
= -0.980785...
170.156250 degrees

Click here to show formula
= -0.985278...
171.562500 degrees

Click here to show formula
= -0.989177...
172.968750 degrees

Click here to show formula
= -0.992480...
174.375000 degrees

Click here to show formula
= -0.995185...
175.781250 degrees

Click here to show formula
= -0.997290...
177.187500 degrees

Click here to show formula
= -0.998795...
178.593750 degrees

Click here to show formula
= -0.999699...
180.000000 degrees-1 = -1.000000...
181.406250 degrees

Click here to show formula
= -0.999699...
182.812500 degrees

Click here to show formula
= -0.998795...
184.218750 degrees

Click here to show formula
= -0.997290...
185.625000 degrees

Click here to show formula
= -0.995185...
187.031250 degrees

Click here to show formula
= -0.992480...
188.437500 degrees

Click here to show formula
= -0.989177...
189.843750 degrees

Click here to show formula
= -0.985278...
191.250000 degrees

Click here to show formula
= -0.980785...
192.656250 degrees

Click here to show formula
= -0.975702...
194.062500 degrees

Click here to show formula
= -0.970031...
195.468750 degrees

Click here to show formula
= -0.963776...
196.875000 degrees

Click here to show formula
= -0.956940...
198.281250 degrees

Click here to show formula
= -0.949528...
199.687500 degrees

Click here to show formula
= -0.941544...
201.093750 degrees

Click here to show formula
= -0.932993...
202.500000 degrees

Click here to show formula
= -0.923880...
203.906250 degrees

Click here to show formula
= -0.914210...
205.312500 degrees

Click here to show formula
= -0.903989...
206.718750 degrees

Click here to show formula
= -0.893224...
208.125000 degrees

Click here to show formula
= -0.881921...
209.531250 degrees

Click here to show formula
= -0.870087...
210.937500 degrees

Click here to show formula
= -0.857729...
212.343750 degrees

Click here to show formula
= -0.844854...
213.750000 degrees

Click here to show formula
= -0.831470...
215.156250 degrees

Click here to show formula
= -0.817585...
216.562500 degrees

Click here to show formula
= -0.803208...
217.968750 degrees

Click here to show formula
= -0.788346...
219.375000 degrees

Click here to show formula
= -0.773010...
220.781250 degrees

Click here to show formula
= -0.757209...
222.187500 degrees

Click here to show formula
= -0.740951...
223.593750 degrees

Click here to show formula
= -0.724247...
225.000000 degrees

Click here to show formula
= -0.707107...
226.406250 degrees

Click here to show formula
= -0.689541...
227.812500 degrees

Click here to show formula
= -0.671559...
229.218750 degrees

Click here to show formula
= -0.653173...
230.625000 degrees

Click here to show formula
= -0.634393...
232.031250 degrees

Click here to show formula
= -0.615232...
233.437500 degrees

Click here to show formula
= -0.595699...
234.843750 degrees

Click here to show formula
= -0.575808...
236.250000 degrees

Click here to show formula
= -0.555570...
237.656250 degrees

Click here to show formula
= -0.534998...
239.062500 degrees

Click here to show formula
= -0.514103...
240.468750 degrees

Click here to show formula
= -0.492898...
241.875000 degrees

Click here to show formula
= -0.471397...
243.281250 degrees

Click here to show formula
= -0.449611...
244.687500 degrees

Click here to show formula
= -0.427555...
246.093750 degrees

Click here to show formula
= -0.405241...
247.500000 degrees

Click here to show formula
= -0.382683...
248.906250 degrees

Click here to show formula
= -0.359895...
250.312500 degrees

Click here to show formula
= -0.336890...
251.718750 degrees

Click here to show formula
= -0.313682...
253.125000 degrees

Click here to show formula
= -0.290285...
254.531250 degrees

Click here to show formula
= -0.266713...
255.937500 degrees

Click here to show formula
= -0.242980...
257.343750 degrees

Click here to show formula
= -0.219101...
258.750000 degrees

Click here to show formula
= -0.195090...
260.156250 degrees

Click here to show formula
= -0.170962...
261.562500 degrees

Click here to show formula
= -0.146730...
262.968750 degrees

Click here to show formula
= -0.122411...
264.375000 degrees

Click here to show formula
= -0.098017...
265.781250 degrees

Click here to show formula
= -0.073565...
267.187500 degrees

Click here to show formula
= -0.049068...
268.593750 degrees

Click here to show formula
= -0.024541...
270.000000 degrees

Click here to show formula
= 0.000000...
271.406250 degrees

Click here to show formula
= 0.024541...
272.812500 degrees

Click here to show formula
= 0.049068...
274.218750 degrees

Click here to show formula
= 0.073565...
275.625000 degrees

Click here to show formula
= 0.098017...
277.031250 degrees

Click here to show formula
= 0.122411...
278.437500 degrees

Click here to show formula
= 0.146730...
279.843750 degrees

Click here to show formula
= 0.170962...
281.250000 degrees

Click here to show formula
= 0.195090...
282.656250 degrees

Click here to show formula
= 0.219101...
284.062500 degrees

Click here to show formula
= 0.242980...
285.468750 degrees

Click here to show formula
= 0.266713...
286.875000 degrees

Click here to show formula
= 0.290285...
288.281250 degrees

Click here to show formula
= 0.313682...
289.687500 degrees

Click here to show formula
= 0.336890...
291.093750 degrees

Click here to show formula
= 0.359895...
292.500000 degrees

Click here to show formula
= 0.382683...
293.906250 degrees

Click here to show formula
= 0.405241...
295.312500 degrees

Click here to show formula
= 0.427555...
296.718750 degrees

Click here to show formula
= 0.449611...
298.125000 degrees

Click here to show formula
= 0.471397...
299.531250 degrees

Click here to show formula
= 0.492898...
300.937500 degrees

Click here to show formula
= 0.514103...
302.343750 degrees

Click here to show formula
= 0.534998...
303.750000 degrees

Click here to show formula
= 0.555570...
305.156250 degrees

Click here to show formula
= 0.575808...
306.562500 degrees

Click here to show formula
= 0.595699...
307.968750 degrees

Click here to show formula
= 0.615232...
309.375000 degrees

Click here to show formula
= 0.634393...
310.781250 degrees

Click here to show formula
= 0.653173...
312.187500 degrees

Click here to show formula
= 0.671559...
313.593750 degrees

Click here to show formula
= 0.689541...
315.000000 degrees

Click here to show formula
= 0.707107...
316.406250 degrees

Click here to show formula
= 0.724247...
317.812500 degrees

Click here to show formula
= 0.740951...
319.218750 degrees

Click here to show formula
= 0.757209...
320.625000 degrees

Click here to show formula
= 0.773010...
322.031250 degrees

Click here to show formula
= 0.788346...
323.437500 degrees

Click here to show formula
= 0.803208...
324.843750 degrees

Click here to show formula
= 0.817585...
326.250000 degrees

Click here to show formula
= 0.831470...
327.656250 degrees

Click here to show formula
= 0.844854...
329.062500 degrees

Click here to show formula
= 0.857729...
330.468750 degrees

Click here to show formula
= 0.870087...
331.875000 degrees

Click here to show formula
= 0.881921...
333.281250 degrees

Click here to show formula
= 0.893224...
334.687500 degrees

Click here to show formula
= 0.903989...
336.093750 degrees

Click here to show formula
= 0.914210...
337.500000 degrees

Click here to show formula
= 0.923880...
338.906250 degrees

Click here to show formula
= 0.932993...
340.312500 degrees

Click here to show formula
= 0.941544...
341.718750 degrees

Click here to show formula
= 0.949528...
343.125000 degrees

Click here to show formula
= 0.956940...
344.531250 degrees

Click here to show formula
= 0.963776...
345.937500 degrees

Click here to show formula
= 0.970031...
347.343750 degrees

Click here to show formula
= 0.975702...
348.750000 degrees

Click here to show formula
= 0.980785...
350.156250 degrees

Click here to show formula
= 0.985278...
351.562500 degrees

Click here to show formula
= 0.989177...
352.968750 degrees

Click here to show formula
= 0.992480...
354.375000 degrees

Click here to show formula
= 0.995185...
355.781250 degrees

Click here to show formula
= 0.997290...
357.187500 degrees

Click here to show formula
= 0.998795...
358.593750 degrees

Click here to show formula
= 0.999699...

Description

Binary cosinus is a function where one waveform period is equal to 1.0 instead of 2.0 * PI. This function and pattern was discovered by Hans Petter Selasky, Norway, in 2021. Generalization of the formula goes like this: The main component of the formula is a square-root series. The binary phase information is encoded as the selection between two function variants.

First variant:
X=1-X2

Second variant:
X=1+X2

The selection of function variant is a so-called Gray-code. That means at most one bit distinguishes between subsequent phase values.

Origin

The pattern is inspired by squaring complex unit vectors.

Implementation

A C-code implementation of binary cosinus can be found here.

--HPS


This document was last updated on Wed 02 Jun 2021 06:57:16 PM CEST.