Question

How do you convert 90 degrees to radians?

Answer 1

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")`

Answer 2

`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"`