Question

Find the degree measures corresponding to the following radian measures:
(i) \[\dfrac{{11}}{{16}}\]
(ii) \[ - 4\]
(iii) \[\dfrac{{5\pi }}{3}\]
(iv) \[\dfrac{{7\pi }}{6}\]

Answer 1

Hint: According to the question, we just have to convert radians into degrees by using the conversion method that is \[1radian = \dfrac{{180}}{\pi }\] degree and use \[\pi = \dfrac{{22}}{7}\].

Formula used:
Here we use the formula, to convert degree into radians that is \[1radian = \dfrac{{180}}{\pi }\] degree where \[\pi = \dfrac{{22}}{7}\] .

Complete step-by-step answer:
(i) \[\dfrac{{11}}{{16}}\] Radians
Here, we will convert radians into degrees.
So, for converting radian into degrees we would have to multiply it by \[\dfrac{{180}}{\pi }\] .
\[\dfrac{{11}}{{16}} = \dfrac{{180}}{\pi } \times \dfrac{{11}}{{16}}\] Degrees
Putting value of \[\pi \] as \[\dfrac{{22}}{7}\]
\[ \Rightarrow \dfrac{{180 \times 11 \times 7}}{{22 \times 16}}\] Degrees
On simplifying we get,
\[ \Rightarrow 39.375\] Degrees
Hence, \[\dfrac{{11}}{{16}}\] Radians = \[39.375\] Degrees
(ii) \[ - 4\] Radians
Here, we will convert radians into degrees.
So, for converting radian into degrees we would have to multiply it by \[\dfrac{{180}}{\pi }\] .
\[ - 4 = \dfrac{{180}}{\pi } \times \left( { - 4} \right)\] Degrees
Putting value of \[\pi \] as \[\dfrac{{22}}{7}\]
\[ \Rightarrow \dfrac{{ - 180 \times 4 \times 7}}{{22}}\] Degrees
On simplifying we get,
\[ \Rightarrow - 229\] Degrees
Hence, \[ - 4\] Radians = \[ - 229\] Degrees
 (iii) \[\dfrac{{5\pi }}{3}\] Radians
Here, we will convert radians into degrees.
So, for converting radian into degrees we would have to multiply it by \[\dfrac{{180}}{\pi }\] .
 \[\dfrac{{5\pi }}{3} = \dfrac{{5\pi \times 180}}{{3 \times \pi }}\] Degrees
Cancelling \[\pi \]from both numerator and denominator:
\[ \Rightarrow \dfrac{{5 \times 180}}{3}\] Degrees
On simplifying we get,
\[ \Rightarrow 300\] Degrees
Hence, \[\dfrac{{5\pi }}{3}\] Radians = \[300\] Degrees
 (iv) \[\dfrac{{7\pi }}{6}\] Radians
Here, we will convert radians into degrees.
So, for converting radians into degrees we would have to multiply it by \[\dfrac{{180}}{\pi }\] .
 \[\dfrac{{7\pi }}{6} = \dfrac{{7\pi \times 180}}{{6 \times \pi }}\] Degrees
Cancelling \[\pi \]from both numerator and denominator:
\[ \Rightarrow \dfrac{{7 \times 180}}{6}\] Degrees
On simplifying we get,
\[ \Rightarrow 210\] Degrees
Hence, \[\dfrac{{7\pi }}{6}\] Radians = \[210\] Degrees
Hence, degree measures for given radian measures are \[39.375\] degrees, \[ - 229\] degrees, \[300\] degrees, and \[210\] degrees.

Note: To solve these types of questions, you just need to use the conversion method that can be of radian to degree to minutes or degree to minutes to second and vice versa. You can also use the conversion formulas that are \[1radian = \dfrac{{180}}{\pi }\] radians, \[{1^ \circ } = 60'\]and \[1' = 60''\]where ‘stands for minutes and ‘’ stands for seconds.