Why do radians disappear

It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. Why is the radians implicitly cancelled? Somehow, the feet just trumps the numerator unit.

For all other cases, you need to introduce the unit conversion fraction, and cancel explicitly. Is it because radians and angles have no relevance to linear speed v , so they are simply discarded? Radians are dimensionless , i. The units make better sense when you view a radius as distance per radian, i. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. Ask Question. Asked 8 years, 8 months ago. Active 6 years, 6 months ago. Viewed 7k times. MJD I considered going that route. It can get annoying if this is not what you intend.

This is not a bad thing per se, but it triples the number of rules dealing with trig, which triples the time it takes to process them all. If X is an angle object, then it's correct because X in any system represents the same angle, but if you plot the derivative vs. X in degrees then the magnitude of the slope is off. Then you have fully implemented ijabbott's idea with no drawbacks.

That's fine unless you interrupt execution at precisely the wrong moment! Wow, you'd have to be really quick to halt it inside the new function, LOL. They're not the same. A plane angle, which is dimensionless, is a scalar value with a unit to reflect a quantity, be it radians, degrees, grads, quadrants, sextants, turns, or some other unit of measure.

Dimensionless and unitless are two very different things. There are an enormous number of dimensionless scalars with units of measure. The SI unit for a plane angle is the rad , the abbreviation for Radian. The unit for a solid angle is the sr , the abbreviation for Steradian.

But is the distinction important mathematically or only for engineering purposes? From what I can gather, mathematicians or at least pure mathematicians tend to think of the trig functions as purely numeric functions, without units.

For example, "trig substitution" may be used to make certain integrals more tractable. Forgive me. I couldn't help myself, but freely admit having committed the Faustian act of selling my soul using the theoretical in practical applications.

The units used are arbitrary, but they're still there. Otherwise they would be polluted with conversion factors, such as 0. In Newtonian Mechanics i. No units are given in physics texts, but you'd best be consistent regarding mass and length, and for the Gravitational Constant G it has units and its value is units dependent , and what that means for the resulting units you get for the mutual Force.

Not too bad if you're dealing with mks vs cgs as it shuffles the decimal point a few places, but it was a mess when some of us had to deal with it in FPS Feet, Pounds and Seconds with someone always giving "r" in miles; see remarks below.

Theoretical mathematicians and physicists like to deal in general cases using range and domain variables independent of units. Doesn't mean they're unitless. It's implicit in practical application that units will either be consistent or conversion factors employed. It makes them cleaner looking for clarity of the relationships. Trig identities are often written without the "theta" but it's implicit.

If you want a real joy, start using common "English" aka "US Engineering" fps foot, pound, second units related to force, mass and energy, using Pounds, Poundals and Slugs for mass and force. Don't even try to use the former British Engineering System which lacked coherence and contained ambiguity regarding what a "pound" is force or mass? Had several years of that to contend with in school. Gave an area answer one other time in Barns and there's a smaller one related to it called a Shed versus square feet.

Ever so glad when metric and S. Hoping this has been at least partially entertaining. The sin , cos , and exp functions all have similar-looking power series expansions except that sin and cos expansions miss every other term of exp and alternate the signs of the remaining terms , so what is special about sin and cos that requires the input to have dimensionless units, but not exp?

English American. Threaded Mode Linear Mode The case of the disappearing angle units, or "the dangle of the angle". Converting between degrees and radians is pretty easy.

In my opinion, the easiest way to remember this is to think of it as canceling out. Although the radian is a unit of measure, it is a dimensionless quantity. Radian measure is the ratio of the length of a circular arc a to the radius of the arc r. Since radian measure is the ratio of a length to a length, the result is a pure number that needs no unit symbol.

This leads us to the rule to convert radian measure to degree measure.