![]() "Degree." Wolfram Language & System Documentation Center. Wolfram Research (1988), Degree, Wolfram Language function, (updated 2002). This slightly unfortunate dual nature of degrees has its roots in the treatment of angular measure by the SI system of units, which treats radians as a dimensionless measure whose explicit specification is optional.Ĭite this as: Wolfram Research (1988), Degree, Wolfram Language function, (updated 2002). Some care is therefore needed in distinguishing the mathematical constant Degree (which relates degrees to radians) and the unit of angular measure itself. Note that the Wolfram Language unit framework represents the angular degree as Quantity for the purposes of unit encoding and conversion.RealDigits can be used to return a list of digits of Degree and ContinuedFraction to obtain terms of its continued fraction expansion. In fact, calculating the first million decimal digits of Degree takes only a fraction of a second on a modern desktop computer due to the rapid convergence of the Chudnovsky formula for Pi. Degree can be evaluated to arbitrary numerical precision using N.While (like Pi) it is not known if Degree is normal (meaning the digits in its base- expansion are equally distributed) to any base, its known digits are very uniformly distributed. As a result of its close relationship with Pi, Degree is known to be both irrational and transcendental, meaning it can be expressed neither as a ratio of integers nor as the root of any integer polynomial.Cos ) may require use of functions such as FunctionExpand and FullSimplify. Cos ) are automatically expanded in terms of simpler functions, expansion and simplification of more complicated expressions involving Degree (e.g. While many expressions involving Degree (e.g. When Degree is used as a symbol, it is propagated as an exact quantity that can be expressed in terms of Pi using FunctionExpand.While most angle-related functions in the Wolfram Language take radian measures as their arguments and return radian measures as results, the symbol Degree can be used as a multiplier when entering values in degree measures (e.g. The use of Degree is especially common in calculations involving plane geometry and trigonometry. Degree has exact value and numerical value. Degree is the symbol representing the number of radians in one angular degree (1 °), which can also be input into the Wolfram Language as ∖.WE could write out the word degrees or just put that symbol there. And you are left with 180 divided by 3, leaving us with what is that? Negative 60, and we don't want to forget the units We could write them out, the only unit left is degrees. The radians cancel out, the pi also cancels. So of course the units are going to work out. This is going to work out: We have however manyradians we have times the number of degrees per radian. Or you can say there are 180 over pi degrees per radian. We need to multiply this by degrees - I'm going to write the word out instead of the circle here - It would be really hard to visualize that, degrees per radian So how many degrees are there per radian? well we know that for 180 degrees we have pi radians. Well, to figure this out we need to know how many degrees there are per radian. Switch to a new color- so negative pi over three, so how do we convert that? So what do we get based on this information right over here. We want to convertnegative pi over three radians. ![]() ![]() If you want to think about it, pi radians are halfway around the circle Halfway around the circle like that, and it is the same thing as 180 degrees. We wanted to convert pi radians, well we just figured out! Pi radians are equal to 180 degrees. Which actually answers the first part of our question. So we get pi radians are equal to 180 degrees. And we have still the units which are degrees. Now can we simplify this a little bit? Well sure, Both two pi and 360 are divisible by two so lets divide things by two, and if we do that, what do we get? Or what are pi radians equal to? Well on the left side here we're just left with pi radians, and on the righthand side here, 360 divided by two is 180. You could literally write degrees instead of that little symbol. Sometimes it doesn't look like a unit but it is a unit. That is equal to 360 degrees Now, can we simplify this? That's a bore to write this little, superscript circle That's literally the units of the question. Now that exact same angle if we were to measure it in degrees, How many degrees is that? Well if you were doing degrees, it would be one full revolution. How many radians is that? Well we know that it is 2 pi radians. And the first question I'll ask you: If you do one revolution, You have an angle that went all the way around once. We're asked to convert pi radians and negative pi/3 radians to degrees.
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