What is the meaning of y = sin(x) over the interval [0,1]?

Question

one thing I don't understand is what is sin(0) and sin(1) exactly? I am alright with the concept of radian (pi) but don't understand 0 and 1. What does it mean?

Answer 1

Generally, unless stated, the interval $[0,1]$ means the range of $x$ is from $0$ radian to $1$ radian.

$\sin 0$ is basically $\sin x|_{x=0}=0$. You can think of $\sin 1 = \sin \frac\pi\pi\approx0.0175$.

This is how it looks like:

Answer 2

I am not completely sure what you are asking but I will try to answer. In the context of the question in the title, $[0,1] $ means that they are talking about $y=\sin x $ for values on $x $ on the closed interval from 0 to 1 (rather than say all of the real numbers.

In terms of what this means, the sin function just maps a real number to another real number so though $\sin x$ may not always be rational, it is always just a real number.

Answer 3

If $1$ is considered as $1$ radian then $1$ less than $\pi /2$ so $sin x$ is a strictly increasing function on that interval.