
How do you express degrees in radian in terms of pi?
Answer
473.1k+ views
Hint: In this question, we have to find out the required from the given particulars.
We need to express the angle given in radian in terms of pi. For that we first need to know the relation between degree and radian and apply that formula by putting the given angle in degree. After solving the result we can find out the required solution.
Formula used:
Degree radian
Complete step by step answer:
The given angle is degree.
We need to express it in radian in terms of pi.
We know, Degree radian
Now applying the formula and by unitary method we can write the angle in radian terms of pi.
Hence, degree Radian
Solving that we get, degree Radian
Hence, expressing degrees in radian in terms of pi, we get, degree Radian.
Note: A degree usually denoted by (the degree symbol) is a measurement of a plane angle in which one full rotation is degrees.
It is not an SI unit —the SI unit of angular measure is the radian —but it is mentioned in the SI brochure as an accepted unit because a full rotation equals radians, one degree is equivalent to radians.
Relation between degree, radian and grade is
In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more "natural" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number .
We need to express the angle given in radian in terms of pi. For that we first need to know the relation between degree and radian and apply that formula by putting the given angle in degree. After solving the result we can find out the required solution.
Formula used:
Complete step by step answer:
The given angle is
We need to express it in radian in terms of pi.
We know,
Now applying the formula and by unitary method we can write the angle in radian terms of pi.
Hence,
Solving that we get,
Hence, expressing
Note: A degree usually denoted by
It is not an SI unit —the SI unit of angular measure is the radian —but it is mentioned in the SI brochure as an accepted unit because a full rotation equals
Relation between degree, radian and grade is
In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more "natural" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number
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