Question

cos-1(cos 4pi/3)

Answer 1

well first you have \(\large \rm cos(4\pi/3)=-1/2 \)

Answer 2

Now we ask what angle gives -1/2
\(\large \rm cos(\theta)=-1/2 \) what is theta

Answer 3

actually you have to be given an interval

Answer 4

\(\large \rm cos(5\pi/6)=-1/2, cos(7\pi/6)=-1/2 \)

Answer 5

and there are other angles that give -1/2

Answer 6

Here depends on what exactly the question is about? they have to give some more info

Answer 7

okay I made a mistake there, let me bring a diagram

Answer 8

what you see is what the instructor gave me,

Answer 9

so we have \(\large \rm cos^{-1}(cos(4\pi/3))\)
I said \(\large \rm cos(4\pi/3)=-1/2\)
now i need to find \(\large \rm cos^{-1}(-1/2)\)
now since the range is \(\large \rm [0, \pi]\)
then there one angle where \(\large \rm cos(x)=-1/2\)
and that's \(\large \rm cos(2\pi/3)=-1/2\)

Answer 10

sorry OP stuck for a moment

Answer 11

the angle you are looking for is 2pi/3
i was trying to draw a picture! but the drawing tool stopped

Answer 12

no its ok, i was only taught with a calculator and all this is foreign to me, and the teacher is all like figure it out your self

Answer 13

are familiar with inverse of sine and cosine
remember they can have the inverse only in restricted domains
like [0, pi] for cosine and [-pi/2, pi/2] for sine

Answer 14

im not failiar with it, i type it in my fancy calculator and out pop the answers

Answer 15

well you should learn to deal with it by hand! Calculator is a bad thing to get used to

Answer 16

when i took college math 1 and 2 the instructor only taught calculator, now i am having to retake college math 2 online and calculator is not a option

Answer 17

that's why you have to work hard learning how to deal with this

Answer 18

you need to know this table pretty well