Convirtiendo entre grados y radianes

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Introduction

Lessons

    Examples

    Lessons

    1. Repaso en conversión de unidades
      1. 24 rosas = ___________ docenas de rosas
      2. 3 docenas de rosas = ___________ rosas
      3. 65 kg = __________ lbs
      4. 100 lbs = __________ kg
      1. Convierte los siguientes ángulos de grados a radianes:
        1. 85°
        2. -213°
        3. 30°
        4. 60°

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      Topic Basics
      180° = π\pi radianes

      What is a radian?

      A radian is a type of unit used for measuring angles. The other unit that you're probably more familiar with when it comes to measuring angles is degrees. While there's more than two units that help depict the measure of an angle, radian and degrees are the two that you'll have to deal with most.

      You're probably wondering why we have to use radians when we already have degrees. That is because degrees are not actually numbers. In order to compute math, we need to work with numbers. A good example that's similar to this concept is using decimals when we have percentages. Although a percentage can be shown with a number followed by a % sign, when we do math, we convert that to a decimal (or fraction).

      In this lesson, we'll learn how to convert radians to degrees, and also the other way around: turning degrees into radians.

      Converting radians to degrees

      To start off, let's first convert radians into units that we're more familiar with: degrees.

      Question

      Convert the following angles from radians to degrees

      1. i) π6\frac{\pi }{6}

      Solution

      Same as converting other units, when converting radians to degrees, we need to know the conversion factor. In a sense, this is the radians to degrees formula that can help you change from one unit to another. In the case of converting radian to degree, the conversion factor is 180π  rad\frac{{180^\circ }}{{\pi \;rad}} .

      Now, we can multiply π6\frac{\pi }{6} with the conversion factor 180π  rad\frac{{180^\circ }}{{\pi \;rad}} . The π\pi and rad cancel out each other, and then only 301\frac{{30^\circ }}{1} is left. So, the final answer is 3030^\circ

      Multiply pi/6 by 180/pi to get the answer of 30 degree
      Convert pi/6 to 30 degree
      1. ii) 5π3 - \frac{{5\pi }}{3}

      Similar to the first part of the question, we multiply 5π3 - \frac{{5\pi }}{3} with the conversion factor 180π  rad\frac{{180^\circ }}{{\pi \;rad}}. Again, the π\pi and rad cancel out each other.  Both The 3 and the 180180^\circ are divided by 3. We have 51601 - \frac{5}{1} \bullet \frac{{60^\circ }}{1} left, and we will then multiply them and get the final answer 300 - 300^\circ

      Convert -5pi/3 to -300 degree
      Convert -5pi/3 to -300 degree

      iii) 2

      We multiply 2 with the conversion factor 180π  rad\frac{{180^\circ }}{{\pi \;rad}}. The rad cancels out each other and leaves 2180π2 \bullet \frac{{180^\circ }}{\pi }. Using the calculator, we are able to get the final answer 114.592114.592^\circ

      convert 2 radian to degree
      Convert 2 radian to degree

      iii) -8.14

      We multiply -8.14 with the conversion factor 180π  rad\frac{{180^\circ }}{{\pi \;rad}}. The rad cancels out each other and leaves us with 8.14180π - 8.14 \bullet \frac{{180^\circ }}{\pi }. Using the calculator, we are able to get the final answer 466.388 - 466.388^\circ

      convert -8.14 radian to degree
      Convert -8.14 radian to degree

      Converting degrees to radians

      Conversely, we can convert degrees to radians. Let's take a look at these sets of questions.

      Question

      Convert the following angles from degrees to radians

      1. i) 8585^\circ

      Solution

      The conversion factor for converting degrees to radian is π  radian180\frac{{\pi \;radian}}{{180^\circ }}

      We can multiply 8585^\circ with π  radian180\frac{{\pi \;radian}}{{180^\circ }}. The degree signs cancel out each out. We have 85π  radian18085 \bullet \frac{{\pi \;radian}}{{180}} left. Multiplying them with a calculator, we get the final answer 1.48 radian.

      Similar questions can be done in the same way as this method we just explored:

      Multiply the degrees with conversion factor π  radian180\frac{{\pi \;radian}}{{180^\circ }} . Use calculator for the multiplication when it is necessary. We will then get the final answer.

      As an online resource, if you wanted to quickly convert between radians and decimals, use this online converter to help you out or double check your work.