156k views
2 votes
Convert 14° into radians manually (no calculator) please show work. Thank you in advance!!

Convert 14° into radians manually (no calculator) please show work. Thank you in advance-example-1
User Robert Bak
by
7.1k points

2 Answers

1 vote

Answer:


\large\boxed{14^o=(7\pi)/(90)\ radians}

Explanation:


\text{The formula for conversion of degrees to radians:}\\\\1^o=(\pi)/(180^o)\ radians\\\\x^o=(x\pi)/(180)\ radians\\\\\text{We have}\ x=14^o.\ \text{Substitute:}\\\\14^o=(14\pi)/(180)=(7\pi)/(90)

User Uragiristereo
by
7.3k points
7 votes

1 degree is
\frac\pi{180} radians. So 14 degrees is
(14\pi)/(180)=(7\pi)/(90) rad.

Easy way to remember this: one complete revolution in a circle is 360 degrees. But it's also
2\pi radians. So the conversion rate is


(2\pi\,\rm rad)/(360^\circ)=(\pi\,\rm rad)/(180^\circ)

i.e. for every
\pi radians there are 180º.

User Uneakharsh
by
6.7k points