
How do you convert degrees into radians?
Answer
471.3k+ views
Hint: In order to convert the degree measure into radian measure, multiply the given degree measure with radians to get the required result. Radian describes the plane angle subtended by a circular arc, as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius of the circle.
Complete step by step solution:
The measure of an angle is controlled by the measure of pivot from the underlying side to the terminal side. In radians, one complete counter clockwise upheaval is and in degrees, one complete counterclockwise upset is . Along these lines, degree measure and radian measure are connected by the condition:
radians
The above condition can also be simplified as follows:
radians
So, we get the condition radians. This leads us to the standard to change over degree measure to radian measure. To change over from degree to radian, multiply the degree measure by radians.
So, in the question we are given degrees.
radians
Multiplying both sides of the equation with .
radians
So, radians.
Therefore, degrees equal to radians.
Note: The radian, indicated by the symbol , is the SI unit for measuring angles, and is the standard unit of angle measure utilized in numerous zones of arithmetic. The length of an arc of a unit circle is mathematically equivalent to the measurement in radians of the angle that it subtends; one radian is degrees. The radian is characterized in the SI similar to a dimensionless value
Complete step by step solution:
The measure of an angle is controlled by the measure of pivot from the underlying side to the terminal side. In radians, one complete counter clockwise upheaval is
The above condition can also be simplified as follows:
So, we get the condition
So, in the question we are given
Multiplying both sides of the equation with
So,
Therefore,
Note: The radian, indicated by the symbol
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