What is the difference between arcsin and csc?
For instance, if arcsin=(sin)^-1, and I were to evaluate arcsin0, (and sin0 is 2π), how would my answer ((2π)^-1) differ from (1/2π)?

Question

What is the difference between arcsin and csc?
For instance, if arcsin=(sin)^-1, and I were to evaluate arcsin0, (and sin0 is 2π), how would my answer ((2π)^-1) differ from (1/2π)?

campbell_st · Answer

cosec is the reciprocal of sin  and arc sin is the inverse funtion

campbell_st · Answer

so with the inverse of sine.... domain of sin becomes the range in arcsin.. and range of sin becomes the domain of arcsin.... restrictions on the domian of arcsin exist..

anonymous · Answer

it is not true that $\sin(0)=2\pi$ but rather $\sin(0)=0$

anonymous · Answer

okay! thanks for the correction! :P totally didn't know what I was thinking there. haha

anonymous · Answer

also i sense some confusion about $\arcsin(x)=\sin^{-1}(x)$ this does not mean the reciprocal, it means the inverse function, so for example $$\sin^{-1}(\frac{\sqrt{3}}{2})=\frac{\pi}{3}$$ because $\frac{\pi}{3}$ is the number in the interval $[-\frac{\pi}{2},\frac{\pi}{2}]$ whose sine is $\frac{\sqrt{3}}{2}$

anonymous · Answer

there was definitely some confusion for me here! thanks for helping clarify.  i appreciate the help! :)