$\sin(25°)+\cos(115°)$?

Question

What is the value of $\sin(25°)+\cos(115°)$?

Using $\cos(90°+\theta)=-\sin(\theta)$, we get, $$\sin(25°)+\cos(115°)=\sin(25°)-\sin(25°)=0$$

But when I searched the same on Google, it showed $-0.45816155531$ as result on their calculator.

Which result is correct? Also, why the other one is incorrect?

For some basic information about writing mathematics at this site see, e.g., here, here, here and here. — Another User, Jun 26 '22 at 10:03
Your argument is correct. The calculator was likely using radians instead of degrees. — preferred_anon, Jun 26 '22 at 10:04
@preferred_anon I feel ashamed but you are correct, should I delete my question? — , Jun 26 '22 at 10:10
I’m voting to close this question because this question does not meet the standards of MSE. — uniquesolution, Jun 26 '22 at 10:11
I've not really closed this because of a lack of context, but more because the reconciliation is another site's conversion from radians to degrees : which is an observation that I find very tangential to the actual solving of the question. — Sarvesh Ravichandran Iyer, Jun 26 '22 at 15:23
@SarveshRavichandranIyer I think this is a fair question. OP encounters a real problem and posted own work together with result from google, which illustrates the issue quite well. Although it's a short post, the quality is acceptable, especially after the edits. If this still lacks context then maybe not many questions on this site have proper context. — WhatsUp, Jun 26 '22 at 15:28
@WhatsUp I'm thinking about this question from a repository point of view. The mistake is Google's , right? It's no fault of the author. Honestly, there is nothing wrong done by the author here, I completely agree with that. But all that is warranted for such effort is a "this is an error committed by Google, not by you" , and we gave that. There is no appropriate close reason for this, hence I closed for lack of context and posted a comment. Once again : the poster did nothing wrong, but this question has no long term value. I will let the reopen queue do justice, however. — Sarvesh Ravichandran Iyer, Jun 26 '22 at 16:10
@SarveshRavichandranIyer can I do something to make it better? — , Jun 26 '22 at 16:15
@MaxWill Let me be completely honest here : you can do nothing on your part to make it better, which sounds funny. The reason is, that the problem with your question actually has nothing to with mathematics per se, although it's a very , very important observation : namely , that Google uses radians by default. I found a small button on the left hand side of the calculator that changes the input to degrees, so that is helpful (although the calculator throws up a floating point error). — Sarvesh Ravichandran Iyer, Jun 26 '22 at 16:17
@SarveshRavichandranIyer Also, if I may, I have a doubts on your site, since MSE is source, wouldn't it be better to include the links to your best answers in your about me section of MSE (some great users have such a thing) and you'll save money from website? [If you don't like me asking here I'll delete comment at once] — , Jun 26 '22 at 16:19
@MaxWill There's no money that I earn from anywhere online. Do not worry, the comments section can be used temporarily for conversation , later on it will be deleted by someone who isn't both of us. — Sarvesh Ravichandran Iyer, Jun 26 '22 at 16:22
@SarveshRavichandranIyer when I put the input in calculator after being pointed out my mistake, thanks to MSE community, then after converting to degrees I was getting $0$ as result. Floating point error was not observed. Here's my search, it might help: [Added in next comment] Also, please note, that I had to type degrees in search bar only then it worked, when clicking on "Deg" in calculator, nothing was happening. — , Jun 26 '22 at 16:23
Here's the link: https://www.google.com/search?q=sin+25+degrees+%2B+cos+115+degrees&rlz=1C1CHBF_enIN829IN829&sxsrf=ALiCzsZu1anET6i9QUx2vS1NFD3TN6LmkQ%3A1656260515757&ei=o4e4YrvtLaWL4-EP7ZiQsAc&ved=0ahUKEwj7ysmdw8v4AhWlxTgGHW0MBHYQ4dUDCA4&uact=5&oq=sin+25+degrees+%2B+cos+115+degrees&gs_lcp=Cgdnd3Mtd2l6EAMyBAghEBU6BwgAEEcQsAM6BAgAEB46BggAEB4QBzoGCAAQHhAIOgQIIRAKOgUIIRCgAToICCEQHhAWEB1KBAhBGABKBAhGGABQvipYvHtg23xoAnABeACAAdEBiAGSGZIBBjAuMjEuMZgBAKABAcgBBsABAQ&sclient=gws-wiz — , Jun 26 '22 at 16:23
@MaxWill Interesting , I actually get the floating point error! Thanks for your input. Anyway, it looks like there are a couple of reopen votes. This is the community at work, so I will leave them to it and depart. I wish you the best , and have voted up your question. — Sarvesh Ravichandran Iyer, Jun 26 '22 at 16:25
I'm talking about your money invested in that website for purchasing domain and keeping it alive via periodic payments. I was suggesting alternative. But if you're passionate and have something else in mind then that I don't know. Many sites are already giving good knowledge of basics. Just curious nothing else. — , Jun 26 '22 at 16:27

score 1 · Accepted Answer · edited Jun 26 '22 at 16:14

1

Your answer is absolutely correct. It is $0$.
In the calculator, you must have used radians that's why you are getting $-0.4581615553$
But in question the value are in degrees.

edited Jun 26 '22 at 16:14

answered Jun 26 '22 at 15:18

Yugandhar Patil

26

$\sin(25°)+\cos(115°)$?

1 Answers1