How do i convert degrees to radians & leave the answer in pi?

Question

I'm awful at math and struggling with my Pre-Calculus homework.

I'm supposed to convert degrees into radians and leave the answers in multiples of pi.

I know I'm supposed to multiply by (pi/180), and using that formula i answered some of the easier questions.

i'm stuck on what you do with bigger numbers, where the answers end up like 2pi/3

how do i get those answers? also, when i use my calculator i obviously end up with a decimal, how do i get the right answer from the decimal?

the ones i'm having trouble with right now are-

150 degrees

270 degrees

480 degrees

etc.

Could someone please explain?

Answer 1

I'll take the first one.

You're right - there are 180 degrees in pi radians, so you'll multiply degrees by pi/180.  (You'll multiply radians by 180/pi.  Whatever you're trying to convert goes in the denominator, and whatever you want as a result goes in the numerator.)

So,

150 (pi/180) = (150/180) pi

Reduce that fraction:

150/180 = 15/18 = 5/6

So 150 degrees = (5/6) pi.

Go, now, and do thou likewise.

Answer 2

wow, this is weird. I'm doin the exact same stuff in my pre-cal class and i have homework tonight on the exact same stuff.

sorry, i'm not good at explaining stuff. so, thats it. oh, but if you dont understand dont get on here just raise your hand and ask the teacher.