Do π/2 = 90 and (pi)3.14/2 = 1.57 represent the same thing? (n is pi sign.)I know π also represents 180 degrees in calculus. If I write π/2, which is 90 degree, is this the same thing as when...

Do π/2 = 90 and (pi)3.14/2 = 1.57 represent the same thing? (n is pi sign.)

I know π also represents 180 degrees in calculus. If I write π/2, which is 90 degree, is this the same thing as when you divide pi 3.1415926/2? (n is pi sign.)

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kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted on

The short answer is no, pi/2 radians and 1.57 radians are not exactly the same thing - though they are close; pi is an irrational number, and as such has no exact decimal representation. Hence, neither does pi/2.

A degree is defined such that exactly 360 form a circle. 360 is a rational number, and can be divided by 4 to get exactly 90 -- one quarter of a circle.

A radian is defined based on the circumference of the circle. A radian is defined as the angle at which the length along the edge of the circle is equal to the radius of the circle. pi is the number of radians in one-half of the circle. You can take a string that is the length of the radius and wrap it on the top of the circle 3.14159265.... times.

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

The symbol used in the question is called pi. The enotes answer facility does not have the facility to represent this symbol, So i will use the description "pi" in my answer.

The constant pi is a universal constant which represents the ratio of the lengths of circumference divided by diameter of any circle. The approximate value of pi 3.14. Thus:

(pi)/2 = 3.14/2 = 1.57

Angles can be measured in degrees or in radians. The relationship between these two units of measurement of angles is given by:

2*pi radians = 360 degrees

Thus

pi radians = 360/2 = 180 degrees

And:

pi/2 radians = 180/2 = 90 degrees.

Thus:

number pi/2 = number 1.57

And:

Angle of pi/2 radians = Angle of 90 degrees

So, yes, though pi is an approximation, 180/2 and pi/2 represent the same thing but in different terminology and with more or less approximation.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

pi radians =180 degree .

Therefore pi/2 = 180/2 = 90 degree.

 pi =3.1459265...is never termiminating  and also not showing any pattern of repetetion of digits.

 22/7,  3.14 or 3.14159 etc  are all approximate to pi but never equal.

pi is  the ratio of the circumference to the diameter (double radius = diameter) of a circle. So the  angle measurements has a close relation with  the circumference and radius.

The value pi is a number  slightly more than 3  but less than 3.2.

pi is not a rational number like p/q, where p and q are integers.

pi is not an algebraic number also.  So cannot be expressed as root of any polynomial with a variable of rational coefficients. It is transcendental  real number.

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