Question

Convert 14° into radians manually (no calculator) please show work. Thank you in advance!!

Answer 1

`\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)`

Answer 2

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.