Answer
Verified
429k+ views
Hint: There are two units of measure for an angle. One is called degree (denoted by \[{}^\circ \] sign). And the other unit of measure is radian, radian is denoted by rad but it is not denoted by using this notation generally. Every angle can either be measured in degree or radian. The measure of angles can also be converted from one unit to another unit. The conversion formula is as follows:
From degree to radian – measure of angle in degree \[\times \dfrac{\pi }{180{}^\circ }\] .
From radian to degree – measure of angle in radian \[\times \dfrac{180{}^\circ }{\pi }\].
Complete step by step answer:
When two lines intersect, they give rise to four different spaces for the point of intersection. These created spaces are called angles. If the rotation is anticlockwise then the angles are said to be positive, and if the rotation is clockwise then the angles are said to be negative. When an object moves through a complete cycle, we say it has covered 360 degrees (360\[{}^\circ \]). Similarly, a radian is an angle made at the center of the circle by an arc that is equal to the length of the radius of that particular circle. From these two definitions, we can say that,
One rotation\[=360{}^\circ =2\pi \]
\[\Rightarrow 360{}^\circ =2\pi \]
Dividing both sides by \[2\pi \], we get
\[\begin{align}
& \Rightarrow \dfrac{360{}^\circ }{2\pi }=\dfrac{2\pi }{2\pi } \\
& \Rightarrow 1rad=\dfrac{180{}^\circ }{\pi } \\
\end{align}\]
From this, we can state the formula for radian to degree conversion as,
Measure of angle in degree = Measure of angle in radian \[\times \dfrac{180{}^\circ }{\pi }\]. This formula is applicable for both positive as well as negative angles.
Note:
This conversion formula should be remembered, as it might become useful in some questions of trigonometry, coordinate geometry etc. Also, its inverse, that is, conversion from radian to degree should be remembered.
From degree to radian – measure of angle in degree \[\times \dfrac{\pi }{180{}^\circ }\] .
From radian to degree – measure of angle in radian \[\times \dfrac{180{}^\circ }{\pi }\].
Complete step by step answer:
When two lines intersect, they give rise to four different spaces for the point of intersection. These created spaces are called angles. If the rotation is anticlockwise then the angles are said to be positive, and if the rotation is clockwise then the angles are said to be negative. When an object moves through a complete cycle, we say it has covered 360 degrees (360\[{}^\circ \]). Similarly, a radian is an angle made at the center of the circle by an arc that is equal to the length of the radius of that particular circle. From these two definitions, we can say that,
One rotation\[=360{}^\circ =2\pi \]
\[\Rightarrow 360{}^\circ =2\pi \]
Dividing both sides by \[2\pi \], we get
\[\begin{align}
& \Rightarrow \dfrac{360{}^\circ }{2\pi }=\dfrac{2\pi }{2\pi } \\
& \Rightarrow 1rad=\dfrac{180{}^\circ }{\pi } \\
\end{align}\]
From this, we can state the formula for radian to degree conversion as,
Measure of angle in degree = Measure of angle in radian \[\times \dfrac{180{}^\circ }{\pi }\]. This formula is applicable for both positive as well as negative angles.
Note:
This conversion formula should be remembered, as it might become useful in some questions of trigonometry, coordinate geometry etc. Also, its inverse, that is, conversion from radian to degree should be remembered.
Recently Updated Pages
Who among the following was the religious guru of class 7 social science CBSE
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Trending doubts
A rainbow has circular shape because A The earth is class 11 physics CBSE
Which are the Top 10 Largest Countries of the World?
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE