Please help me with this

Question

Convert the angle given in radians to degrees.

Round your answer to three decimal places if needed.

37 radians = °

Answer 1

37 radians * 180 degrees / pi radians =

37*180/pi degrees = 6660/pi degrees

Now here's the trick... pi is ABOUT 22/7 = 3.142857142857142857....

and they are APPROXIMATELY equal..

so 6600 / pi =

6600 divided by 22/7 =

6600 * 7/22 = <-- dividing fractions, KFC: keep, flip, change

6600/1 * 7/22 =

3300 * 7/11 <--- reduces by 2

300*7 <--- reduces by 11

= 2100 degrees an APPROXIMATE answer...

-----------------------------------------------------

The windows calculator says,

37*180/pi = 37*180/ 3.1416 <--- 3 digit rounding

requires carrying 4 digits

2,119.9388846447669977081741787624

which to 3 digits is 2119.939

---------------------------------

Unfortunately, the irrational PI in the denominator cannot

be rationalized out.

Both are valid approximations, with the latter being closer

to the actual answer

Answer 2

The conversion factor that should be memorized is 180/π deg/rad

37 rad • 180/π deg/rad ≈ 2119.944°

The best way to remember when converting degrees to radians or radians to degrees is to include the units and verify that one of the units will cancel out.

Answer 3

37 rads ⁄1 × 360^°⁄ 2∏ rads = 2,120^°