
How do you convert 285 degrees to radians?
Answer
453k+ views
Hint: The measurement of angles can be done in two different units namely radian and degree. In geometry, we measure the angles in degree but also in radians sometimes, similarly in trigonometry, we measure the angle in radians but sometimes in degrees too. So, there are different kinds of units for determining the angle that are, degrees and radians. There is a simple formula to convert a given degree into radians (vice versa). Using that formula, we can find out the correct answer.
Complete step-by-step solution:
The value of \[{180^0}\] is equal to \[\pi \]radians.
Then \[{1^0}\] is equal to \[\dfrac{\pi }{{180}}\] radians.
So the given \[{x^0}\] is equal to \[x \times \dfrac{\pi }{{180}}\] radians.
This is the general formula for converting the angel in degrees to radians.
Now We have, \[{285^0}\].
Using the formula
\[ \Rightarrow {285^0} = 285 \times \dfrac{\pi }{{180}}{\text{ radians}}\]
\[ \Rightarrow \dfrac{{285\pi }}{{180}}\].
To cancel this we find the factors of 285 and 180.
That is, \[285 = 3 \times 5 \times 19\]
\[ \Rightarrow 180 = 2 \times 2 \times 3 \times 3 \times 5\]
Then we have,
\[ \Rightarrow \dfrac{{3 \times 5 \times 19}}{{2 \times 2 \times 3 \times 3 \times 5}}\pi \]
Cancelling we have
\[ \Rightarrow \dfrac{{19\pi }}{{12}}\].
Hence \[{285^0}\] is \[\dfrac{{19\pi }}{{12}}\] rad.
We can put it in the decimal form, that is we know that the value of \[\pi \] is 3.142.
Substituting and simplifying we have,
\[ \Rightarrow \dfrac{{19 \times 3.142}}{{12}}\]
\[ \Rightarrow 4.975\].
Hence \[{285^0}\] is 4.975 rad.
Note: We know that the radian is denoted by ‘rad’. Suppose if they ask us to convert \[\dfrac{{19\pi }}{{12}}\]rad into degree. The value of \[\pi \] radian is equal to \[{180^0}\].
Then 1 rad is equal to \[\dfrac{{180}}{\pi }\] degrees.
So the given \[x\] rad is equal to \[x \times \dfrac{{180}}{\pi }\] degrees.
This is the general formula for converting the angle in radians to degrees.
Then \[\dfrac{{19\pi }}{{12}}\] rad becomes
\[\Rightarrow \dfrac{{19\pi }}{{12}} = \dfrac{{19\pi }}{{12}} \times \dfrac{{180}}{\pi }\] degree
\[ \Rightarrow \dfrac{{19 \times 180}}{{12}}\]
\[ \Rightarrow 19 \times 15\]
\[ \Rightarrow {285^0}\].
Hence \[\dfrac{{19\pi }}{{12}}\]rad is equal to \[{285^0}\] .
Complete step-by-step solution:
The value of \[{180^0}\] is equal to \[\pi \]radians.
Then \[{1^0}\] is equal to \[\dfrac{\pi }{{180}}\] radians.
So the given \[{x^0}\] is equal to \[x \times \dfrac{\pi }{{180}}\] radians.
This is the general formula for converting the angel in degrees to radians.
Now We have, \[{285^0}\].
Using the formula
\[ \Rightarrow {285^0} = 285 \times \dfrac{\pi }{{180}}{\text{ radians}}\]
\[ \Rightarrow \dfrac{{285\pi }}{{180}}\].
To cancel this we find the factors of 285 and 180.
That is, \[285 = 3 \times 5 \times 19\]
\[ \Rightarrow 180 = 2 \times 2 \times 3 \times 3 \times 5\]
Then we have,
\[ \Rightarrow \dfrac{{3 \times 5 \times 19}}{{2 \times 2 \times 3 \times 3 \times 5}}\pi \]
Cancelling we have
\[ \Rightarrow \dfrac{{19\pi }}{{12}}\].
Hence \[{285^0}\] is \[\dfrac{{19\pi }}{{12}}\] rad.
We can put it in the decimal form, that is we know that the value of \[\pi \] is 3.142.
Substituting and simplifying we have,
\[ \Rightarrow \dfrac{{19 \times 3.142}}{{12}}\]
\[ \Rightarrow 4.975\].
Hence \[{285^0}\] is 4.975 rad.
Note: We know that the radian is denoted by ‘rad’. Suppose if they ask us to convert \[\dfrac{{19\pi }}{{12}}\]rad into degree. The value of \[\pi \] radian is equal to \[{180^0}\].
Then 1 rad is equal to \[\dfrac{{180}}{\pi }\] degrees.
So the given \[x\] rad is equal to \[x \times \dfrac{{180}}{\pi }\] degrees.
This is the general formula for converting the angle in radians to degrees.
Then \[\dfrac{{19\pi }}{{12}}\] rad becomes
\[\Rightarrow \dfrac{{19\pi }}{{12}} = \dfrac{{19\pi }}{{12}} \times \dfrac{{180}}{\pi }\] degree
\[ \Rightarrow \dfrac{{19 \times 180}}{{12}}\]
\[ \Rightarrow 19 \times 15\]
\[ \Rightarrow {285^0}\].
Hence \[\dfrac{{19\pi }}{{12}}\]rad is equal to \[{285^0}\] .
Recently Updated Pages
Master Class 10 General Knowledge: Engaging Questions & Answers for Success

Master Class 10 Computer Science: Engaging Questions & Answers for Success

Master Class 10 Science: Engaging Questions & Answers for Success

Master Class 10 Social Science: Engaging Questions & Answers for Success

Master Class 10 Maths: Engaging Questions & Answers for Success

Master Class 10 English: Engaging Questions & Answers for Success

Trending doubts
Truly whole mankind is one was declared by the Kannada class 10 social science CBSE

Explain the three major features of the shiwaliks class 10 social science CBSE

Distinguish between the reserved forests and protected class 10 biology CBSE

What is the corona radiata penetrating enzyme class 10 biology CBSE

What are the public facilities provided by the government? Also explain each facility

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
