How do you convert 90 degrees to radians?

2 Answers
Apr 9, 2018

Multiply by a fraction which represents 1 revolution in both degrees and radians, you will find that #90^@=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^@# and #2pi# 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"#

#color(green)(=pi/2" rad")#

Apr 9, 2018

#pi/2#

Explanation:

#"to convert from "color(blue)"degrees to radians"#

#color(red)(bar(ul(|color(white)(2/2)color(black)("radians "="degrees "xxpi/180)color(white)(2/2)|)))#

#rArrcancel(90^@)^1xxpi/cancel(180^@)^2=pi/2" radians"#