Discover the inverse trigonometric functions Learn how to find the inverse of the sine function I first learned that arcsin and inverse sine are two ways of saying the same thing But then i was thinking about the inverse sine function being a function, so it must be limited in it's range fr. You'd better say that their effects cancel out or compensate each other $\arcsin (\sin x)=x$, so that the composition of the two functions is neutral (at least in some range).
Sorry for asking such question I have a very basic understanding of $\\arcsin, \\arccos, \\arctan$ functions I do know how their graph looks like and not much more beyond that I am wondering if $\arcsin x$ has an equivalent, perhaps in logarithms Can we find the inverse of the above equation? How can i find the arc sine of a sine without using a calculator
3 By definition, $\arcsin (x)$ is the angle $\alpha$ such that $\sin (\alpha) = x$ and $-\pi/2 \le \alpha \le \pi/2$, while $\arccos (x)$ is the angle $\beta$ such that $\cos (\beta) = x$ and $0 \le \beta \le \pi$. Since $-\pi/2 \le \alpha \le \pi/2$, $\cos (\alpha) \ge 0$, so we have $\cos (\alpha) = \sqrt {1 - x^2}$.
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