How do you convert 90 degrees to radians?

Apr 9, 2018

Multiply by a fraction which represents 1 revolution in both degrees and radians, you will find that ${90}^{\circ} = \frac{\pi}{2}$ radians

Explanation:

To convert from degrees to radians, consider a common measurement to determine a conversion fraction ratio.

1 revolution about a circle is both ${360}^{\circ}$ and $2 \pi$ radians, so if we wanted to represent this as an equation:

360" deg"=2pi " rad" rArr 1=(2pi " rad")/(360" deg")

color(red)(rArr 1=(pi" rad")/(180" deg")

That above equation gives you a conversion from degrees to radians. We can now plug in the angle we want to convert units with:

90cancel(" deg")xxcolor(red)((pi" rad")/(180cancel(" deg")))=?

90xx(pi" rad")/(180)=90/180xxpi" rad"

$\textcolor{g r e e n}{= \frac{\pi}{2} \text{ rad}}$

Apr 9, 2018

$\frac{\pi}{2}$

Explanation:

$\text{to convert from "color(blue)"degrees to radians}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\text{radians "="degrees } \times \frac{\pi}{180}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow {\cancel{{90}^{\circ}}}^{1} \times \frac{\pi}{\cancel{{180}^{\circ}}} ^ 2 = \frac{\pi}{2} \text{ radians}$