Trigonometry question

[trumpet-205]

The qn is incorrect. argument useless and therefore should be dropped... alongwith this topic. My friend gave me an incorrect question.

So do you have the correct equation?

PS: As far as I know only when people study Geometry that they use degree the most. Once you get past that, it is radians all the way. Radians is part of the SI system, degree and gradians are not.

 

[Niksy]

Enter sin(90) into your calculator and then enter sin(90°). Then tell me what you get. I've said this before: radians must be converted to numeric degrees before you can take the sine of them. And it is not accepted: that's what your teacher tells you. Your teacher means that you should be able to convert degrees into radians and back again when dealing with a circle or any other geometric shape: get this through your thick skull.

Jeez, I'm getting blasted for solving a mathematical equation by using actual variables instead of writing a long paragraph. I didn't see any of you 'math experts' doing this.

Inputing sin(90) in the calculator on my Android phone yealds 0.89399666 as a result. Googling sin(90) gives a similar result, just a little bit more precise. Googling sin(90 degrees) on the other hand gives me 1.

Also, I've been doing some Android game programmin recently and almost everything there is done in radians. Sin() and Cos() functions both take parameters in radians. Rotation functions on the other hand take degrees as parameters.

May I ask what your education is? I believe that's where the discrepancy comes from. As I said, I'm a high school student (12th grade) and while we were introduced to trigonometry though angles, we currently work 90% the time in radians.

 

[calmwaters]

Inputing sin(90) in the calculator on my Android phone yealds 0.89399666 as a result. Googling sin(90) gives a similar result, just a little bit more precise. Googling sin(90 degrees) on the other hand gives me 1.

Also, I've been doing some Android game programmin recently and almost everything there is done in radians. Sin() and Cos() functions both take parameters in radians. Rotation functions on the other hand take degrees as parameters.

May I ask what your education is? I believe that's where the discrepancy comes from. As I said, I'm a high school student (12th grade) and while we were introduced to trigonometry though angles, we currently work 90% the time in radians.

Yeah: when I input sin 90, it gives me .89399666. But that's because I have the radian button selected. When I have the degree button selected, it gives me 1. Glad you agree with me on that.

And I'm not interested in what you do on your Android. So obviously the sine and cosine functions can take numbers and convert them to radians or degrees.

Education discrepancy? Fine. I was home schooled through high school and graduated with a diploma. And, have you noticed how public education is getting worse in this country? Kids are stupider now than they were 10 years ago. And the fact you can write game programs on your Android doesn't mean shit when you can't even properly construct English phrases. You get force fed tons of shit and since you've never seen this information before, you just blindly accept it so you don't have to develop the ability to think. I can think: I've had four years of developing this skill. If you need more proof of this, watch Judge Judy and see how many stupid people your age are on there.

 

[Fat D]

Well since radians are the standard in calculus, then you've got to be able to convert them from degrees since degrees are used in all the other maths.

There is a reason I dislike the term "mathematics", because it makes it sound like each field of the subject is a distinct "mathematic" from each other, as if arithmetic and algebra and calculus are entirely different matters, rather than just different tools from the same box.

And it makes sense to use radians when you input numbers, because degrees are arbitrarily fixed to 360 in a full rotation, whereas radians are a natural unit following directly from unit circle arc length. If there is any competing unit for radians, it should be revolutions, not degrees. And convention has it that radians are used, in most major programming languages and in common calculators that do not distinguish between different modes for different angle units[*]. Because it makes for easier derivation, integration and series expansion. Basically, 1 rad is defined as 1, 1° is defined as pi/180 and 1 revolution is defined as 2*pi.

Spelling out rad after a number is still a good idea though. If you are too lazy to put in a degree sign (which the US-English keyboard makes needlessly difficult, considering you also need it for most everyday temperature scales), you can also use the sind function and its likes, which are trigonometric functions that interpret a number without specified unit as degrees, instead of radians. It is common in programming, where a degree sign might be unavailable, undesirable or hard to interpret, it is less common in writing, where a degree sign is quite literally a non-effort.

Finally, in complex algebra, radians are also the only really usable choice for the imaginary part of the argument to the exponential function.

Basically, every time the trigonometric functions have any other purpose than just calculating a geometric angle, radians are vastly superior to degrees. With degrees, it is pretty much like with powers of ten (or powers of a thousand) - they are good for putting things on an intuitively understandable scale, but they have no real natural basis to them. There are alternatives to both, powers of e and radians, which are easy to math with, totally natural and hard to visualize, and powers of two and revolutions, which are rather visualizable, somewhat natural, but still not as suited to calculus and algebra.

[*] If your calculator does have degree and radian mode, the degree sign most likely is only there to do base-60-digit seperation, like for minutes and seconds, so if you want to enter 50° 3' 45" it becomes 50°3°45.