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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.
Convert the following angles from radians to degrees
- i) 6π
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 πrad180∘ .
Now, we can multiply 6π with the conversion factor πrad180∘ . The π and rad cancel out each other, and then only 130∘ is left. So, the final answer is 30∘
- ii) −35π
Similar to the first part of the question, we multiply −35π with the conversion factor πrad180∘. Again, the π and rad cancel out each other. Both The 3 and the 180∘ are divided by 3. We have −15∙160∘ left, and we will then multiply them and get the final answer −300∘
We multiply 2 with the conversion factor πrad180∘. The rad cancels out each other and leaves 2∙π180∘. Using the calculator, we are able to get the final answer 114.592∘
We multiply -8.14 with the conversion factor πrad180∘. The rad cancels out each other and leaves us with −8.14∙π180∘. Using the calculator, we are able to get the final answer −466.388∘
Converting degrees to radians
Conversely, we can convert degrees to radians. Let's take a look at these sets of questions.
Convert the following angles from degrees to radians
- i) 85∘
The conversion factor for converting degrees to radian is 180∘πradian
We can multiply 85∘ with 180∘πradian. The degree signs cancel out each out. We have 85∙180πradian 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 180∘πradian . 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.