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How do you convert \[\dfrac{2}{3}\pi \] radians to degrees?

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Last updated date: 20th Jun 2024
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Answer
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Hint: We need to know the formula for converting the radian measures into degree measures. We need to substitute the given radian value in that formula. By using arithmetic operations we can easily find the answer. We need to find the final answer in degree measures, so we need to know the degree value \[\pi \].

Complete step-by-step solution:
In this question, we would convert the radian term \[\dfrac{2}{3}\pi \] to a degree. For that, the formula which is given below will help us.
The formula for converting radian measures to degree measures is,
Degree \[ = \]Radian\[ \times \dfrac{{{{180}^ \circ }}}{\pi }\]\[ \to equation\left( 1 \right)\]
So, we would find
\[\dfrac{{2\pi }}{3}\]Radian\[ \to ?\] degree
In this problem we have the radian value, we would convert it into degree value.
We have,
Radian \[ = \dfrac{{2\pi }}{3}\]
So, the equation\[\left( 1 \right)\] becomes,
\[equation\left( 1 \right) \to \] Degree\[ = \]Radians\[ \times \dfrac{{{{180}^ \circ }}}{\pi }\]
Degree\[ = \dfrac{{2\pi }}{3}\]\[ \times \dfrac{{{{180}^ \circ }}}{\pi }\]
We know that \[\left( {\pi = {{180}^ \circ }} \right)\].
\[\pi \] in the numerator and\[\pi \] the denominator can be cancelled each other. So we do not need to substitute the value of\[\pi \]in-degree measures. So, we get
Degree\[ = \dfrac{2}{3} \times {180^ \circ }\]
By solving the above equation, we get
Degree\[ = 2 \times {60^ \circ }\]
Degree\[ = {120^ \circ }\]
So, the final answer is,
\[\dfrac{{2\pi }}{3} = {120^ \circ }\]

Note: Note that this problem can also be solved by substituting the value of\[\pi \]is equal to\[{180^ \circ }\]in the given problem. By using this method we can easily find the answer. This type of questions involves the operation of addition/ subtraction/ multiplication/ division. Note that each radian value must be in the form of\[\pi \] and in each degree value the degree symbol will be present on that term. To make an easy calculation first we would try to cancel the term\[\pi \]in the formula, next we can easily find the answer using normal multiplication and division.