Question

How do you convert `-3.5` to degrees?

Answer 1

use the conversion `pi=180`

Explanation:

-3.5 is a radian measure which needs to be converted to degrees.

for that we need a simple conversion factor: `pi=180`

Now we are going to setup an equation with the conversion factor. A nice way to do this is to take advantage of the proportionality of the problem. So we set the equations up like this:

`-3.5 = x` in the same proportion as `pi=180`

`-3.5/pi=x/180`

to solve we simply undo the division on `x` with a multiply

`180*-3.5/pi=x`

`-630/pi=x`
now it is a matter of how many decimals. Let us say that we are using the standard 3.14 approximation and need two decimal places.

`-630/3.14=x`
`x=-200.64`
(we changed the direction at the end to follow convention)

this should make sense because 3.5 is a little bigger than 3.14 and 200 is a little bigger than 180. And don't forget the sign!

NOTE: always put the same units in the same fraction
`(rad)/(rad)=(degrees)/(degrees)`

and that makes us happy. :)