# Uses of $\pi$ value in trignometery

We use $\pi = 180$ degree in radian and degree relation why we not use the value of $\pi = 3.14$ in degree and radian relation? confused

• The value of $\pi$ is not $3.14$. – egreg Dec 7 '16 at 15:24
• Pi is a Greek letter used to denote the ratio of a circle's circumference and diameter; pie is a type of cake. – Asaf Karagila Dec 7 '16 at 15:24
• Are you just asking about units? A foot is twelve inches. Similarly, $\pi$ radians is $180$ degrees. We could define other units by whatever ratio we like. – lulu Dec 7 '16 at 15:27
• @AsafKaragila Pie is not cake... – David Mitra Dec 7 '16 at 15:27
• @David: I guess it's a cultural thing. In Israel it's considered a cake. At least things like an apple pie and the likes of it. Shepherd's pie is not a cake, that is true. – Asaf Karagila Dec 7 '16 at 15:31

Radians are just a unit that we use to measure angles with. It's about 60 degrees. ($\approx57$)

Degrees are another unit used to measure angles. It is much smaller than a radian. Radians and degrees can be thought of like meters and inches.

And just like $39.4$ inches and $1$ meter represent the same length, $\pi$ (the number 3.14...) radians and 180 degrees represent the same angle. $\pi$ still represents the number 3.14... when dealing with radians. It is just set up so that that many radians and 180 degrees are equivalent.

Note the difference between

1 ) $\pi = 180°$

and

2 ) $\pi$ radians $= 180°$

1) is wrong.