How do you convert #-3.5# to degrees?

Question

Dylan Arnold · Accepted Answer

use the conversion #pi=180#

It is necessary to convert the radian measurement of -3.5 to degrees.

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

Now that we have an equation setup with the conversion factor, we can make good use of the problem's proportionality. To do this, we set up the equations as follows:

#-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)

Given that 200 is a little larger than 180 and 3.5 is a little larger than 3.14, this should make sense. Don't forget about the sign!

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

and that brings us joy. :)

Caroline Adams · Answer

undefined To convert -3.5 to degrees, you multiply by 180 and then divide by π:

$$ \text{Degrees} = (-3.5) \times \frac{180}{\pi} $$

$$ \text{Degrees} \approx -200.67^\circ $$