Numerical Value of Pie
Approximate value of pie is 22/7. This value is correct to 2 decimal places.
The fraction 355/113 is a more correct value and this is correct to 6 decimal
places.
[To remember the fraction 355/113, write down each of 1, 3, 5 in pairs and divide the last three digits by the first three.]
Approximate value of pie, correct to 10 decimal places, is 3.1415926536.
Remember that 1/pie = 0.31831 (approximately.)
Definition of radian
A radian is the measure of an angle at the centre of a circle subtended by an arc equal in length to the radius of the circle.
Let O be the centre of a circle of radius r and the circular arc AB be equal in length to the radius r of the circle.
Then by the definition of a radian, angle AOB = 1 radian.
[To remember the fraction 355/113, write down each of 1, 3, 5 in pairs and divide the last three digits by the first three.]
Approximate value of pie, correct to 10 decimal places, is 3.1415926536.
Remember that 1/pie = 0.31831 (approximately.)
Definition of radian
A radian is the measure of an angle at the centre of a circle subtended by an arc equal in length to the radius of the circle.
Let O be the centre of a circle of radius r and the circular arc AB be equal in length to the radius r of the circle.
Then by the definition of a radian, angle AOB = 1 radian.
An important
Theorem : Radian is a constant angle
Let PQR be a circle with centre O and radius r. Consider an arc AB of the circle so that the length of the arc and that of the radius r are equal. Join O and A and also O and B. Produce AO to meet the circumference of the circle at C.
It is evident, from the construction that angle AOB = 1 radian.
We know that the angle at the centre of a circle is proportional to the length of the corresponding arc.
Thus, angle AOB / angle AOC = arc AB / arc ABC
or angle AOB / 2 right angles = r /{(1/2) x circumference } =r/pie r
or angle AOB /2 right angles = 1/pie
Therefore angle AOB = 2 rt angles /pie = 180 degree/pie.
Thus, one radian = 180 degree/pie
or pie radians = 180 degree.
Therefore 180 degree/pie is not dependent on the radius of a circle and hence it is a constant quantity.
In other words, in any circle, the value of 180 degree/pie is always the same.
Hence, one radian = 180 degree/pie = a constant quantity.
Let PQR be a circle with centre O and radius r. Consider an arc AB of the circle so that the length of the arc and that of the radius r are equal. Join O and A and also O and B. Produce AO to meet the circumference of the circle at C.
It is evident, from the construction that angle AOB = 1 radian.
We know that the angle at the centre of a circle is proportional to the length of the corresponding arc.
Thus, angle AOB / angle AOC = arc AB / arc ABC
or angle AOB / 2 right angles = r /{(1/2) x circumference } =r/pie r
or angle AOB /2 right angles = 1/pie
Therefore angle AOB = 2 rt angles /pie = 180 degree/pie.
Thus, one radian = 180 degree/pie
or pie radians = 180 degree.
Therefore 180 degree/pie is not dependent on the radius of a circle and hence it is a constant quantity.
In other words, in any circle, the value of 180 degree/pie is always the same.
Hence, one radian = 180 degree/pie = a constant quantity.
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