Question

Arcsin(sin(2π)/3) = (2π)/3
True or false
i dont see how it can be but ive been wrong before.

Answer 1

true
impute in calculator

Answer 2

Normally this is true,
A composition of a function and it's inverse should give you the argument back.
Example:\[\Large\rm f(f^{-1}(x))=x\]

But when we're dealing with inverse trig functions, they have their range restricted.

Answer 3

Arcsine is restricted to quadrants 1 and 4.
So it will give us back the reference angle of 2pi/3 in the first quadrant.

Answer 4

Reread it, the fraction is outside of the sine function

Answer 5

Oh the 3 is outside? Oh interesting :o

Answer 6

Could be a typo on their side, but easier to argue later than "oh well i assumed you made a typo"

Answer 7

\[\Large\rm \arcsin\left[\frac{\color{orangered}{\sin(2\pi)}}{3}\right]=\arcsin\left[\frac{\color{orangered}{0}}{3}\right]=\arcsin\left[0\right]\]Arcsine of 0 is simply..... 0, yes? :)

Answer 8

Yep, so it has to be false

Answer 9

Even if it was a typo, it's false in both cases :)
So you should be ok either way.

Answer 10

thanks!:)