Question

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

Answer 1

1 degree is $\dfrac\pi{180}$ radians. So 14 degrees is $\dfrac{14\pi}{180}=\dfrac{7\pi}{90}$ 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

$\dfrac{2\pi\,\rm rad}{360^\circ}=\dfrac{\pi\,\rm rad}{180^\circ}$

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

Answer 2

Answer:

$\large\boxed{14^o=\dfrac{7\pi}{90}\ radians}$

Step-by-step explanation:

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