Question

How do I find the inverse of sin((8pi)/3)

Answer 1

\[\sin(\frac{8\pi}{3})\] is a number, so it makes no sense to ask for its "inverse"

Answer 2

\(\bf sin^{-1}\left(sin\left(\frac{8\pi}{3}\right)\right) \quad ?\)

Answer 3

maybe you are being asked for
\[\sin^{-1}\left(\sin(\frac{8}{3})\right)\]

Answer 4

jdoe, that is what I am asking, sorry if I did not make it clear

Answer 5

you can
a) find the number,then take the inverse sine of it or
b) find the angle between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) that has the same sine

Answer 6

well.... my understanding is that \(\bf sin^{-1}\left(sin\left(\theta\right)\right) = \theta\)

Answer 7

not unless \(-\frac{\pi}{2}\leq \theta\leq \frac{\pi}{2}\)

Answer 8

the answer has to be between those two numbers, otherwise there would be an infinite number of choices and the function would not be well defined

Answer 9

so is the answer \[(\sqrt{3})/2\] ? My homework counted it as wrong

Answer 10

oh no

Answer 11

\[\sin(\frac{8\pi}{3})=\frac{\sqrt3}{2}\]

Answer 12

you want the arcsine of that

Answer 13

Oh, so inverse sine of that would be \[\frac{ \pi }{ 3 }\], right?

Answer 14

yes
see picture above or use a calculator or unit circle

Answer 15

your answer should be the reference angle to \(\bf \cfrac{8\pi}{3}\) between \(\bf -\cfrac{\pi}{2} \ and \ \cfrac{\pi}{2}\)

Answer 16

Ok, so next time I need to make sure sin is in the right domain, then take inverse sine of that answer, right?

Answer 17

so, \(\bf sin^{-1}\left(sin\left(\frac{8\pi}{3}\right)\right) = \cfrac{8\pi}{3}\)
but with the range restrictions of \(\bf sin^{-1}\)you'd