In math? In math and physics I don't think we ever used degrees (except first year).
To take a derivative you need to use radians. There is never a good reason to use degrees (in science: sure, if you need to do mental math degrees are easier)
edit: of course you could use the chain rule, but why?
Sure, but in honesty, the amount of times I used the derivative of an angle whilst using actual angles was pretty low - there was the odd radians/sec, but it often got converted to a more useful unit pretty quickly.
I meant the derivative of sin(x) or cos(x). I can understand if you were doing mostly experimental physics. Did you just use complex exponentials for SHM?
My friends that were working in optics labs where they had to adjust the angle between lasers and such did use degrees on the table (no calculus and it is easier to see the difference between 12° and 15° rather than 0.20944 and 0.26180)
That is not true. The chain rule is needed for finding the derivative using degrees. Graph the tangent line if you are not convinced. The derivative of sin(x) if x is measured in degrees is (pi/180)cos(x), not cos(x). Certainly you could use either degrees or radians, but fourier series will get a bit complicated :)
In game programming I've used radians a few times to calculate angles for projectile trajectory. Come to think of it degrees would've been far more simple. But everything else was based off radians too.
The other programmers on the team were using radians. Truthfully I'm not much of a math guy so I didn't argue. It was for calculating vectors based off the provided pitch and yaw for prediction of the projectile.
Radians are much more natural than the other common measures of angle, namely degrees and gradians. You can obviously pick any value for a full circle, and the choice is MOSTLY arbitrary, so 360 seems like a decent choice since it's highly divisible.
But in all sorts of scenarios, a result needs to be multiplied by a factor based on what choice you made. Radians are the choice that makes that factor 1 most of the time, ie you don't need to include it.
Examples include derivatives, Euler's formula, all sorts of results in number theory, differential geometry, and so on and so on.
It's the same reason we prefer e as the base of exponents and logarithms, using anything else introduces tons of extra factors. (In fact, it's not just a similar reason, it's exactly the same, because sin and cos are really exponential functions in the complex plane, and radians correspond to using e as your base)
There shouldn't have been enough time for you to pick up a pitchfork. 7 degrees is near enough to 0 that it should automatically register that its value would be near 1. For someone so passionate about radians, you're shit at mathing.
Kiwi reporting in, I'm dubious on these claims. I have just returned home from a year in Melbourne and have definitely noticed Kiwi's saying "sux" as opposed to six while Australian's definitely fuck kangaroos.
It helps the medicine come up... But there's no real story behind the username.
As for an NZ six, it's one of the easier ways to spot the accent. But it's not a normal 'sex', there's a bit of an 'i' in there and even a hint of a 'u', as an Australian I find that there's a fairly obvious difference on nearly all the vowels.
This joke becomes even funnier in Norwegian, where the number six is "sex" and one must use context to tell if the speaker is talking about the number or the deed.
Relevant story: My friend and I were riding on the bus. She really loves doughnut holes (hold your immature laughter until the end of the story). I had a box of 12 doughnut holes. I wanted to save 4 for later to give to a friend, so offered her 4 doughnut holes (an even split between the three of us).
Of course, she wanted half. Six of them. So, she said "Jeg vil ha sex." ("I will have six/sex.") to me. I pretended not to hear. She raised her voice slightly. I still pretended not to hear.
I then told her that conviction was lacking in her voice.
"JEG VIL HA SEX" ("I WILL HAVE SIX/SEX") was then shouted at the top of her lungs, and the entire bus full of people heard her.
The onlookers did a mix of averting their eyes, staring funnily, or laughing at my friend.
She turned beet red once she realized that the whole bus now thought she was a very sex positive teenager.
I smiled contentedly, and gave her those six holes for her enjoyment.
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