Question

how do you convert between radians and degrees?

Answer 1

\(\LARGE\color{blue}{ \tt{Degree} \times\frac{π}{180}=radians }\)

Answer 2

\(\LARGE\color{blue}{ \tt{radians} \times\frac{180}{π}=degree }\)

Answer 3

multiply with pi/180

Answer 4

that explains why i got themn wrong i was doing them backwards

Answer 5

it helps (for me) to remember 2 pi radians in a circle and 360º in a circle
\[ \frac{2 \pi \ radians}{ 360 \ degrees} = \frac{ \pi \ radians}{ 180 \ degrees} \]

to convert we *always* multiply by pi/180 or by 180/pi

to figure out which one, we want the "old" measures to "divide out"

example
if you have 180 degrees, we want to "divide by degrees" (think "cancel")
to divide by degrees we multiply by pi/180 because the 180 degrees is in the bottom

Answer 6

what exactly is the purpose of having two different measurements?

Answer 7

example 2:
we have pi radians. convert to degrees

we want to "get rid of" or "cancel" the radians. that means we want to divide by radians.
to do that , multiply by 180/pi (because the radians are in the bottom)

Answer 8

** the purpose of having two different measurements?***

the degrees (minutes, seconds) for measuring angles is *very* old (thousands of years old!)
it has lasted so long because it's convenient. 360 can be divided evenly by 2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120, 180

radians are *very* useful when we want to treat angles as simple numbers (as in a series expansion of sin(x) ). You won't see this use until you get into calculus

Answer 9

ok that makes sense ive started working with sin, cos, tan but very little. im taking college make up classes for the classes i did cruddy in the first time around.

Answer 10

good luck.