Why is it displaying negative value?
Hi friends when i tried to execute the following command
it is displaying the following answer.....
sql> select cos(60) from dual;
COS(90)
-.44807362
what's the reason to display negitive value for cos(60).....
As anish pointed out, most computer languages tend to work in radians rather than degrees....
SQL> CREATE FUNCTION radians(p_degrees IN NUMBER) RETURN NUMBER IS
2 pi NUMBER(9,7) := 3.1415926;
3 BEGIN
4 -- There are 2*PI radians in a circle
5 -- Therefore 2*PI = 360 degrees
6 -- Therefore PI = 180 degrees
7 RETURN (p_degrees/180)*pi;
8 END;
9 /
Function created.
SQL> with t as (select rownum-1 as degrees from dual connect by rownum <= 360)
2 select t.degrees,
3 round(sin(radians(t.degrees)),6) SIN,
4 round(cos(radians(t.degrees)),6) COS
5 from t;
DEGREES SIN COS
0 0 1
1 .017452 .999848
2 .034899 .999391
3 .052336 .99863
4 .069756 .997564
5 .087156 .996195
6 .104528 .994522
7 .121869 .992546
8 .139173 .990268
9 .156434 .987688
10 .173648 .984808
11 .190809 .981627
12 .207912 .978148
13 .224951 .97437
14 .241922 .970296
15 .258819 .965926
16 .275637 .961262
17 .292372 .956305
18 .309017 .951057
19 .325568 .945519
20 .34202 .939693
21 .358368 .93358
22 .374607 .927184
23 .390731 .920505
24 .406737 .913545
25 .422618 .906308
26 .438371 .898794
27 .45399 .891007
28 .469472 .882948
29 .48481 .87462
30 .5 .866025
31 .515038 .857167
32 .529919 .848048
33 .544639 .838671
34 .559193 .829038
35 .573576 .819152
36 .587785 .809017
37 .601815 .798636
38 .615661 .788011
39 .62932 .777146
40 .642788 .766044
41 .656059 .75471
42 .669131 .743145
43 .681998 .731354
44 .694658 .71934
45 .707107 .707107
46 .71934 .694658
47 .731354 .681998
48 .743145 .669131
49 .75471 .656059
50 .766044 .642788
51 .777146 .62932
52 .788011 .615661
53 .798636 .601815
54 .809017 .587785
55 .819152 .573576
56 .829038 .559193
57 .838671 .544639
58 .848048 .529919
59 .857167 .515038
60 .866025 .5
61 .87462 .48481
62 .882948 .469472
63 .891007 .453991
64 .898794 .438371
65 .906308 .422618
66 .913545 .406737
67 .920505 .390731
68 .927184 .374607
69 .93358 .358368
70 .939693 .34202
71 .945519 .325568
72 .951057 .309017
73 .956305 .292372
74 .961262 .275637
75 .965926 .258819
76 .970296 .241922
77 .97437 .224951
78 .978148 .207912
79 .981627 .190809
80 .984808 .173648
81 .987688 .156434
82 .990268 .139173
83 .992546 .121869
84 .994522 .104528
85 .996195 .087156
86 .997564 .069756
87 .99863 .052336
88 .999391 .0349
89 .999848 .017452
90 1 0
91 .999848 -.017452
92 .999391 -.034899
93 .99863 -.052336
94 .997564 -.069756
95 .996195 -.087156
96 .994522 -.104528
97 .992546 -.121869
98 .990268 -.139173
99 .987688 -.156434
100 .984808 -.173648
101 .981627 -.190809
102 .978148 -.207912
103 .97437 -.224951
104 .970296 -.241922
105 .965926 -.258819
106 .961262 -.275637
107 .956305 -.292372
108 .951057 -.309017
109 .945519 -.325568
110 .939693 -.34202
111 .93358 -.358368
112 .927184 -.374607
113 .920505 -.390731
114 .913545 -.406737
115 .906308 -.422618
116 .898794 -.438371
117 .891007 -.45399
118 .882948 -.469472
119 .87462 -.48481
120 .866025 -.5
121 .857167 -.515038
122 .848048 -.529919
123 .838671 -.544639
124 .829038 -.559193
125 .819152 -.573576
126 .809017 -.587785
127 .798636 -.601815
128 .788011 -.615661
129 .777146 -.62932
130 .766044 -.642788
131 .75471 -.656059
132 .743145 -.669131
133 .731354 -.681998
134 .71934 -.694658
135 .707107 -.707107
136 .694658 -.71934
137 .681998 -.731354
138 .669131 -.743145
139 .656059 -.75471
140 .642788 -.766044
141 .62932 -.777146
142 .615662 -.788011
143 .601815 -.798635
144 .587785 -.809017
145 .573576 -.819152
146 .559193 -.829038
147 .544639 -.838671
148 .529919 -.848048
149 .515038 -.857167
150 .5 -.866025
151 .48481 -.87462
152 .469472 -.882948
153 .453991 -.891007
154 .438371 -.898794
155 .422618 -.906308
156 .406737 -.913545
157 .390731 -.920505
158 .374607 -.927184
159 .358368 -.93358
160 .34202 -.939693
161 .325568 -.945519
162 .309017 -.951057
163 .292372 -.956305
164 .275637 -.961262
165 .258819 -.965926
166 .241922 -.970296
167 .224951 -.97437
168 .207912 -.978148
169 .190809 -.981627
170 .173648 -.984808
171 .156435 -.987688
172 .139173 -.990268
173 .121869 -.992546
174 .104529 -.994522
175 .087156 -.996195
176 .069757 -.997564
177 .052336 -.99863
178 .0349 -.999391
179 .017452 -.999848
180 0 -1
181 -.017452 -.999848
182 -.034899 -.999391
183 -.052336 -.99863
184 -.069756 -.997564
185 -.087156 -.996195
186 -.104528 -.994522
187 -.121869 -.992546
188 -.139173 -.990268
189 -.156434 -.987688
190 -.173648 -.984808
191 -.190809 -.981627
192 -.207912 -.978148
193 -.224951 -.97437
194 -.241922 -.970296
195 -.258819 -.965926
196 -.275637 -.961262
197 -.292372 -.956305
198 -.309017 -.951057
199 -.325568 -.945519
200 -.34202 -.939693
201 -.358368 -.93358
202 -.374607 -.927184
203 -.390731 -.920505
204 -.406737 -.913545
205 -.422618 -.906308
206 -.438371 -.898794
207 -.45399 -.891007
208 -.469472 -.882948
209 -.48481 -.87462
210 -.5 -.866025
211 -.515038 -.857167
212 -.529919 -.848048
213 -.544639 -.838671
214 -.559193 -.829038
215 -.573576 -.819152
216 -.587785 -.809017
217 -.601815 -.798636
218 -.615661 -.788011
219 -.62932 -.777146
220 -.642788 -.766044
221 -.656059 -.75471
222 -.669131 -.743145
223 -.681998 -.731354
224 -.694658 -.71934
225 -.707107 -.707107
226 -.71934 -.694658
227 -.731354 -.681998
228 -.743145 -.669131
229 -.75471 -.656059
230 -.766044 -.642788
231 -.777146 -.62932
232 -.788011 -.615662
233 -.798635 -.601815
234 -.809017 -.587785
235 -.819152 -.573576
236 -.829038 -.559193
237 -.838671 -.544639
238 -.848048 -.529919
239 -.857167 -.515038
240 -.866025 -.5
241 -.87462 -.48481
242 -.882948 -.469472
243 -.891006 -.453991
244 -.898794 -.438371
245 -.906308 -.422618
246 -.913545 -.406737
247 -.920505 -.390731
248 -.927184 -.374607
249 -.93358 -.358368
250 -.939693 -.34202
251 -.945519 -.325568
252 -.951056 -.309017
253 -.956305 -.292372
254 -.961262 -.275637
255 -.965926 -.258819
256 -.970296 -.241922
257 -.97437 -.224951
258 -.978148 -.207912
259 -.981627 -.190809
260 -.984808 -.173648
261 -.987688 -.156435
262 -.990268 -.139173
263 -.992546 -.121869
264 -.994522 -.104529
265 -.996195 -.087156
266 -.997564 -.069757
267 -.99863 -.052336
268 -.999391 -.0349
269 -.999848 -.017452
270 -1 0
271 -.999848 .017452
272 -.999391 .034899
273 -.99863 .052336
274 -.997564 .069756
275 -.996195 .087156
276 -.994522 .104528
277 -.992546 .121869
278 -.990268 .139173
279 -.987688 .156434
280 -.984808 .173648
281 -.981627 .190809
282 -.978148 .207912
283 -.97437 .224951
284 -.970296 .241922
285 -.965926 .258819
286 -.961262 .275637
287 -.956305 .292372
288 -.951057 .309017
289 -.945519 .325568
290 -.939693 .34202
291 -.93358 .358368
292 -.927184 .374607
293 -.920505 .390731
294 -.913545 .406737
295 -.906308 .422618
296 -.898794 .438371
297 -.891007 .45399
298 -.882948 .469471
299 -.87462 .48481
300 -.866025 .5
301 -.857167 .515038
302 -.848048 .529919
303 -.838671 .544639
304 -.829038 .559193
305 -.819152 .573576
306 -.809017 .587785
307 -.798636 .601815
308 -.788011 .615661
309 -.777146 .62932
310 -.766045 .642788
311 -.75471 .656059
312 -.743145 .669131
313 -.731354 .681998
314 -.71934 .694658
315 -.707107 .707107
316 -.694658 .71934
317 -.681998 .731354
318 -.669131 .743145
319 -.656059 .75471
320 -.642788 .766044
321 -.62932 .777146
322 -.615662 .788011
323 -.601815 .798635
324 -.587785 .809017
325 -.573577 .819152
326 -.559193 .829038
327 -.544639 .838671
328 -.529919 .848048
329 -.515038 .857167
330 -.5 .866025
331 -.48481 .87462
332 -.469472 .882948
333 -.453991 .891006
334 -.438371 .898794
335 -.422618 .906308
336 -.406737 .913545
337 -.390731 .920505
338 -.374607 .927184
339 -.358368 .93358
340 -.34202 .939693
341 -.325568 .945519
342 -.309017 .951056
343 -.292372 .956305
344 -.275637 .961262
345 -.258819 .965926
346 -.241922 .970296
347 -.224951 .97437
348 -.207912 .978148
349 -.190809 .981627
350 -.173648 .984808
351 -.156435 .987688
352 -.139173 .990268
353 -.121869 .992546
354 -.104529 .994522
355 -.087156 .996195
356 -.069757 .997564
357 -.052336 .99863
358 -.0349 .999391
359 -.017453 .999848
360 rows selected.
SQL>
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<removed_by_moderator>
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Why is zero showing as a negative value?
Does anyone know why zero is showing as a negative value?
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Not really a bug, just a limitation of the mathematics involved.
You're entering the numbers as base 10 numerals. Computers work in base 2, so before any calculation is done, each number must be converted to its base 2 representation.
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Each of the "zeros" in your sums involves several pieces of data in the sum, not all of which can be expressed exactly in base 2. In two of the sums, the errors (if any) cancel out and there is no difference between the sum expressed to two decimal places and the same sum expressed to 15 digits. In the other three, this is not true, as can be seen below.
The image is of your test table. Columns A, B, and C have been reduced i width, all non-sum rows have been hidden to reduce the image size, and the SUM cells have been set to show 30 places (the maximum permited in Numbers) after the decimal to ensure that all significant places are shown, and that the decimal points are lined up for easy comparison.
Note that three of the results differ from their displayed (two decimal place) values. The largest difference is in the third value, the smallest in the forth. The absolute difference between expected and actual result in the third of these lies between the other two, but is more noticeable because the result is less than zero and carries the - sign because of that. The minus sign is not "inserted" (randomly) by the software; it's there for the same reason there's a minus sign in the cell containing -103.31 is in that cell: the value in the cell is negative.
"If I replace the cells containing the duplicates eg. £269.57, £90.11 & £103.31 with numbers manually added together £539.14, £180.22, £206.62. - the software doesn't insert the negative."
Nor does it "insert the negative" in the first cell displaying a "zero" result, or the cell displaying a 26.04 result. Replacing those six numbers with six (or three) others changes the translation errors for each of these pieces of the sum, and that changes the sum itself. In this case the cumulative error moved the result from being 'smaller' than expected to 'larger' than expected. The result is now slightly larger than zero, so the minus sign is not needed or appropriate.
Here are two further examples. The sum shown is the one in row 130. The data is the same as in the original table except for rows 126 and 127.
Original values:
Two occurrences of -90.11 replaced with a 0 and -180.22 produced this change in the result. Still negative, so the minus sign wi still be there.
Two occurrences of -90.11 replaced with -90.10 and 90.12:
A surprise! The actual value is zero (to the limits of precision of the underlying math).
But that's not (for the usual user) a predictable result.
Depending what you are doing with the results, you may want to do the rounding proposed by Wayne. This will change the actual vaue in the cell to the displayed value ( 0.00), and will remove the minus sign.
It's not a bug—Numbers follows ISO standards in its math—but you may wish to Provide Numbers Feedback to Apple regarding your (and others) user expectations. You'll find an item with that name in the Numbers menu in Numbers.
Regards,
Barry
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