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Find the conversion of \[ - 115\] degrees to radians

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Last updated date: 22nd Feb 2024
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IVSAT 2024
Answer
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Hint: Degrees and radians are two different units that are used for the measurement of the angles. The conversion of degrees to radians is considered while measuring the angles in geometry. The measure of the angle is denoted by degrees, having the symbol \[^ \circ \] .The value of \[{180^ \circ }\] equals to \[\pi \] radians. For converting any given angle from the measure of its degrees to the radian, we need to multiply the value by \[\dfrac{\pi }{{180}}\] .

Complete step-by-step answer:
Angle in radians=angle in degrees \[ \times \dfrac{\pi }{{180}}\]
First we need to Jot down the degrees that we want to convert into radians.
Then we need to multiply the degrees by \[\dfrac{\pi }{{180}}\] .
Here we need to convert \[ - 115\] degrees to radians,
Hence we have,
 \[ - 115 \times \dfrac{\pi }{{180}}\]
Now simply we can carry out the multiplication by multiplying the degrees by \[\frac{\pi }{{180}}\] . Think of it as if we are multiplying two fractions. The first fraction consists of the degrees in the numerator and 1 as the denominator, and the second fraction consists of \[\pi \] in the numerator and has \[180\] in the denominator. This makes calculation easy.
Hence we have,
 \[ \Rightarrow \dfrac{{ - 115\pi }}{{180}}\]
The last step is to simplify. Now, we have to put each fraction in its lowest terms to get the final answer. We need to find the largest number which can evenly divide to the numerator and the denominator of each fraction and use it for simplifying the fraction.
Hence after conversion of \[ - 115\] degrees to radians we have \[ - 2.0071\] radians substituting the value of pi as 3.14.
So, the correct answer is “ \[ - 2.0071\] radians”.

Note: In geometry both degree and radian represent the measure of an angle. One complete anticlockwise revolution can be represented by \[2\pi \] in radians or \[360\] in degrees. Radian is commonly considered while measuring the angles of trigonometric functions or periodic functions. Radians are always represented in terms of pi.