Question

Help with Radians? Please??

Answer 1

basically pi radians = 180 degrees

Answer 2

Well I ment on a specific question.

Answer 3

ok

Answer 4

"Change 28 degrees to radians." And show all work if you can please, I'd like to try to understand it abit better.

Answer 5

Mainly i don't need you to answer it directly, but i'd like help on how to do it

Answer 6

180 degrees = pi radians
1 degree = pi/180

so
23 degrees = (pi/180) * 23 radians

Answer 7

do you follow the above solution?

Answer 8

Except for the fact that radians always seem to have a pi in them, they are really not too strange. 1 radian is close to 57º (it is exactly 180/pi degrees. If you use a calculator you will be 57.2957.... degrees)

so these problems are the same kind as changing feet to inches (1 foot is 12 inches), for example.

Answer 9

so remember this ratio
\[ \frac{ 180 \text{ deg}}{\pi \text{ radians}} \]
if you have an angle measured in radians you multiply by that number to get degrees

if you have an angle measured in degrees you multiply by pi/180 (notice we flipped it) to get radians

Answer 10

I'm very lost ._.

Answer 11

you need to know a few things.

1) how to multiply a number times a fraction

Can you do

\[ 1 \text{ radian} \cdot \frac{ 180 \text{ deg}}{\pi \text{ radians}} \]
?

Answer 12

57.32, roundedup, but how would I apply this to my question? Would I change the 180 to 28?

Answer 13

as you may notice you don't get an *exact* answer (the calculator only show the first 9 decimals or so... but they go on forever ... how annoying)
so people just write 180/pi degrees for an exact answer, or 57.32 if they want "close" answer.

But here is the important idea. notice in
\[ 1 \text{ radian} \cdot \frac{ 180 \text{ deg}}{\pi \text{ radians}} \]
the units (the words radian and deg)
can be treated as if they were numbers. I mean radian/radian can be thought of as 1 ( anything divided by itself is 1).
we are left with just deg


so we know
\[ 1 \text{ radian} \cdot \frac{ 180 \text{ deg}}{\pi \text{ radians}} = \frac{180}{\pi} \text{ deg}\]

Answer 14

so the idea is if you start with radians,
multiply by the ratio
\[ \frac{ 180 \text{ deg}}{\pi \text{ radians}} \]
and you will get degrees
if they want an exact answer, leave it with the pi
if they want a decimal, use a calculator

Answer 15

now let's do it the other way
you have degrees and want radians

Answer 16

"Change 28 degrees to radians.

we start with 28 degrees
and multiply by the "magic ratio" flipped:
\[ 28 \text{ deg} \cdot \frac{\pi \text{ radians}}{ 180 \text{ deg}} \]

notice that the units (the words) deg/deg divide out (become 1 or "cancel")
and you are left with radians

Answer 17

you get
\[ \frac{28 \pi }{ 180 } \text{ radians} \]

of course we should simplify the 28/180
we can divide top and bottom by 4 to get
7/45
so the exact answer is
\[ \frac{7 \pi }{ 45 } \text{ radians} \]

Answer 18

That all made my brain hurt, but i think I understand now. I can use those formula's whenever i get the given degree's/Radians?

Answer 19

a radian is about 57 degrees, so we should expect 28 degrees to be close to ½ of a radian

Answer 20

practice a few problems. remember the ratio

\[ \frac{ 180 \text{ deg}}{\pi \text{ radians}} \]
or
\[ \frac{\pi \text{ radians}}{ 180 \text{ deg}} \]

and use the version that "cancels" the old unit, and leaves the new unit.

Answer 21

Thank you so much for dealing with me XD. I'm a history person not a math person, and this was very helpful!