So what do we get? This becomes, let me just rewrite it. All of that over , so this is equal to, and we get it in radians. And so, if we simplify it, let's see, we can divide the numerator and the denominator both by, looks like, So if you divide the numerator by 30, you get five. You divide the denominator by 30, you get six.
Now let's do the same thing for negative 45 degrees. What do you get for negative 45 degrees if you were to convert that to radians? Same exact process. You have negative, and I'll do this one a little quicker. Negative 45 degrees. I'll write down the word. Times, times pi radians, pi radians for every degrees. The degrees cancel out, and you're left with negative 45 pi over radians.
So this is equal to negative 45 pi over , over radians. How can we simplify this? Well it looks like they're both, at minimum, divisible by nine, nine times five is 45, this is nine times 20, so actually it's gonna be divisible by more than just, let's see The term radians is like kilometres while degrees is like miles. A radian is an angle measure based on the radius of a circle.
A positive angle in degrees or radians is in the counter-clockwise direction while negative angles are in the clockwise direction. In a scientific calculator, angles are in degrees when the calculator is in degree mode specified by DEG at the top of the calculator screen.
If the calculator screen has RAD, the angles are in radians. Radians measure angles by distance traveled.
So we divide by radius to get a normalized angle:. Moving 1 radian unit is a perfectly normal distance to travel. Strictly speaking, radians are just a number like 1.
Now divide by the distance to the satellite and you get the orbital speed in radians per hour. This formula only works when x is in radians! Well, sine is fundamentally related to distance moved , not head-tilting. Now imagine a car with wheels of radius 2 meters also a monster. Wow -- the car was easier to figure out than the bus!
No crazy formulas, no pi floating around — just multiply to convert rotational speed to linear speed. All because radians speak in terms of the mover. The reverse is easy too. How fast are the wheels turning? Time for a beefier example. It originated in France as the 'grade' along with other metric units. I only know of the French artillery actually using it. Angular measurement in degrees or radians is given in reference to a circle, degrees or 2 Pi radians being the measure one full revolution.
If we were to divide a circle into anything other than deg we would have to change our calendars too - the ancient Greeks worked out that there were days in the year, and that, therefore, we progress about the sun at one degree per day - they were quite close given that they worked on observation alone!
Peter Clark, Cambridge, UK The degree is an arbitrary unit; basically any division of a circle would work as a system of measurement. There is a more fundamental unit call the Radian.
This is the angle subtended by an arc of a circle equal in length to its radius. Since the circumference of a circle is 2 x pi x radius one there are 2 pi, or 6. This is fine for calculations on angular motion but difficult to work out in your head. Ray Gallagher, Belfast, Northern Ireland We inherited degrees from the Babylonians, but many ancient societies were highly interested in astronomy and in some megalithic Britain? This is logical, since the earth turns on its axis times a year.
Their measurements seem to have been interrelated and not arbitrary as a metrically divided circle would be. The Babylonians probably reduced this to as it divides so much more easily by many factors.
After some time struggling to get it to work, I noticed that the scale on which horizontal angles were measured read degrees rather than My supervisor told me that this was and old piece of equipment, once part of an attempt to metricise the circle.
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