clearvars,clc
clearvars,clc
% for a=1:1000
% disp([a abs(sind(3*a)^cotd(2*a))])
% end
for a=0:5:500
disp([a abs(sind(3*a))^cotd(2*a)])
end
The non-commented portion, run after the commented part, produced:
0 0
5 0.000468744510142266
10 0.148911035737121
15 0.548656307656194
20 0.842465074946181
25 0.97132894304139
30 1
35 0.987461071195453
40 0.974955884553554
45 1
50 1.13000329600064
55 1.63550508776103
60 Inf
65 3.10852701803366
70 2.28430230931237
75 1.82263465496624
80 1.48468109599613
85 1.21727324766708
90 1
95 0.821508237297184
100 0.673545317372725
105 0.548656307656194
110 0.437770428162385
115 0.321695772370209
120 0
125 0.611431910229626
130 0.884953170967949
135 1
140 1.02568743452214
145 1.01269815000339
150 1
155 1.0295173505989
160 1.18699282586151
165 1.82263465496624
170 6.71541900873851
175 2133.35831857848
180 0
185 0.000468744510142266
190 0.148911035737121
195 0.548656307656194
200 0.842465074946181
205 0.97132894304139
210 1
215 0.987461071195453
220 0.974955884553554
225 1
230 1.13000329600064
235 1.63550508776103
240 Inf
245 3.10852701803366
250 2.28430230931237
255 1.82263465496624
260 1.48468109599613
265 1.21727324766708
270 1
275 0.821508237297184
280 0.673545317372725
285 0.548656307656194
290 0.437770428162385
295 0.321695772370209
300 0
305 0.611431910229626
310 0.884953170967949
315 1
320 1.02568743452214
325 1.01269815000339
330 1
335 1.0295173505989
340 1.18699282586151
345 1.82263465496624
350 6.71541900873851
355 2133.35831857848
360 0
365 0.000468744510142266
370 0.148911035737121
375 0.548656307656194
380 0.842465074946181
385 0.97132894304139
390 1
395 0.987461071195453
400 0.974955884553554
405 1
410 1.13000329600064
415 1.63550508776103
420 Inf
425 3.10852701803366
430 2.28430230931237
435 1.82263465496624
440 1.48468109599613
445 1.21727324766708
450 1
455 0.821508237297184
460 0.673545317372725
465 0.548656307656194
470 0.437770428162385
475 0.321695772370209
480 0
485 0.611431910229626
490 0.884953170967949
495 1
500 1.02568743452214
showing 30°, 45°, 135° and 150° satisfy the equation. So do increments by multiples of 180°.
The 90° and its multiples are spurious, resulting from Matlab's interpretation of 1^(-infinity) as being 1. This was discovered by asking Wolfram Alpha to solve the equation and not finding the radian equivalent of 90°. But Wolfram Alpha neglected to show the addition of arbitrary integral multiples of pi.
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Posted by Charlie
on 2025-05-12 13:58:49 |
solution
