Question

Find the radian measures corresponding to the following degree measures:
(i) ${25^ \circ }$
(ii) $- {47^ \circ }30'$
(iii) ${240^ \circ }$
(iv) ${520^ \circ }$

Answer 1

According to the question, we just have to convert degree into radians by using the conversion method that is ${1^ \circ } = \dfrac{\pi }{{180}}$ radians and use $\pi = 3.14$. Part (ii) has degrees as well as minutes so convert it into degrees by using ${1^ \circ } = 60'$and hence calculate the values.

Formula used:
Here we use the formula, to convert the degree into radians that is ${1^ \circ } = \dfrac{\pi }{{180}}$ radians where $\pi = 3.14$ .

Complete step-by-step answer:
(i) ${25^ \circ }$
Here, we will convert degrees into radians.
So, for converting the degree into radian we would have to multiply it by $\dfrac{\pi }{{180}}$ .
${25^ \circ } = \dfrac{\pi }{{180}} \times 25$ Radians
Putting value of $\pi$ as 3.14
$\Rightarrow \dfrac{{3.14 \times 25}}{{180}}$ Radians
On simplifying we get,
$\Rightarrow 0.4361$ Radians
(ii) $- {47^ \circ }30'$
We know that, ${1^ \circ } = 60'$
So, $30' = {0.5^ \circ }$
Therefore, $- {47^ \circ }30' = - {47.5^ \circ }$
Here, we will convert degrees into radians.
So, for converting degree into radian we would have to multiply it by $\dfrac{\pi }{{180}}$
Now, Similarly,
$- {47.5^ \circ } = \dfrac{\pi }{{180}} \times ( - 47.5)$ Radians
Putting value of $\pi$ as 3.14
$\Rightarrow \dfrac{{3.14 \times ( - {{47.5}^ \circ })}}{{180}}$ Radians
On simplifying we get,
$\Rightarrow -0.8286$ Radians
(iii) ${240^ \circ }$
Here, we will convert degrees into radians.
So, for converting the degree into radian we would have to multiply it by $\dfrac{\pi }{{180}}$ .
${240^ \circ } = \dfrac{{\pi \times 240}}{{180}}$ Radians
Putting value of $\pi$ as 3.14
$\Rightarrow \dfrac{{3.14 \times 240}}{{180}}$ Radians
On simplifying we get,
$\Rightarrow 4.186$ Radians
(iv) ${520^ \circ }$
Here, we will convert degrees into radians.
So, for converting the degree into radian we would have to multiply it by $\dfrac{\pi }{{180}}$ .
${520^ \circ } = \dfrac{{\pi \times 520}}{{180}}$ Radians
Putting value of $\pi$ as 3.14
$\Rightarrow \dfrac{{3.14 \times 520}}{{180}}$ Radians
On simplifying we get,
$\Rightarrow 9.071$ Radians
Hence, radian measures for given degree measures are $0.4361$ radians, $-0.8286$ radians, $4.186$ radians, and $9.071$ radians.

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