When you’re solving a problem where you have to convert radians to degrees, look at the numbers closely. Be careful though, because while radians are usually written as multiples of π, this isn’t always the case. Simply multiply π/2 by 180/ π to get 90 degrees. For instance, let’s say you have to convert 1/2 π radians into degrees. So, in order to convert radians to degrees, all you have to do is multiply the number of radians by 180 divided by π. That means that 1 radian is equal to 180 degrees divided by π. First, remember that π radians is equal to 180 degrees, or half the number of degrees in a circle. Converting radians to degrees is pretty easy. But if I need to find the area of a sector of a circle, I'd rather you gave me the numerical radian measure that I can plug directly into the formula, rather than the degree measure that I'd have to convert first.Radians and degrees are both units that you can use to measure an angle. If you're describing directions to me, I'd really rather you said, "Turn sixty degrees to the right when you pass the orange mailbox", rather than, "Turn (1/3)π radians" at that point. For the math to make sense, the "numerical" value corresponding to 360° needed to be defined as (that is, needed to be invented having the property of) " 2π is the numerical value of 'once around' a circle."Įach of radians and degrees has its place. For reasons you'll learn later, mathematicians like to work with the "unit" circle, being the circle with r = 1. You know that the circumference C of a circle with radius r is given by C = 2π r. Why is the value for one revolution in radians the irrational value 2π? Because this value makes the math work out right. The 360° for one revolution ("once around") is messy enough. Something similar is going on here (which will make more sense as you progress further into calculus, etc). Yes, " 83%" has a clear meaning, but to do mathematical computations, you first must convert to the equivalent decimal form, 0.83. This is somewhat similar to the difference between decimals and percentages. Why do we have to learn radians, when we already have perfectly good degrees? Because degrees, technically speaking, are not actually numbers, and we can only do math with numbers. (Click "Tap to View Steps" to be taken directly to the Mathway site for a paid upgrade.) Please accept "preferences" cookies in order to enable this widget. Just as "hours" can be expressed as decimal hours or else as "hours - minutes - seconds", so also "degrees" can be expressed as decimal degrees or else as "degrees - minutes - seconds", denoted as "DMS". These units, just as for "hours", are called "minutes" and "seconds". But just as "1.75" hours can be expressed as " 1 hour and 45 minutes", so also "degrees" can be expressed in terms of smaller units. When you work with degrees, you'll almost always be working with decimal degrees that is, with degrees expressed as decimal numbers such as 43.1025°. When you're doing graphs and drawings involving measured angles, you'll be starting with 0° being "east" (it'll actually be the x-axis), and you'll rotate anti-clockwise. Whatever convention your book uses should be specifically defined in the book ask your instructor, if it isn't otherwise clear.Īnd yes, this way of measuring direction (namely, starting at north and moving clockwise) is different from how you'll be measuring angles. These mean " 36 degrees west of north" and " 27 degrees east of south", respectively. Another way of giving directions using degress is of the form N36°W or S27☎. Note: When directions are given in terms of degrees, the direction is (usually) found by starting at "north", being 0°, and moving clockwise by the number of degrees given.
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