what is the range of y=Arc sin x?
I don't know what is the Arc stands for. Please help and explain. Thanks!
ARC means the angle..
arcsin means the angle whose sine is ...x
arccos means the angle whose cosine is ..
so, for this problem, the range is -1 to 1?
y is the angle. Wouldn't it range from -inf to + inf? (4n+1)*PI/2 for all n ?
check my thinking.
I still don't get it. How come y is the angle?
The original equation, I read:
y is the angle whose sine is x
y=arcsin x
so how can i solve for it?
Where is sine x=1?
90?
The function "Arc sin x" is also known as the inverse sine function or the arcsine function. It is denoted as y = sin^(-1)(x) or y = asin(x).
To understand the range of the arcsine function, it is important to first understand the domain and range of the sine function. The sine function (sin x) takes an angle (x) as input and returns the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. The sine function has a range between -1 and +1.
The arcsine function is the inverse of the sine function. It takes a value (x) as input and returns the angle (in radians) whose sine is equal to that value. The arcsine function has a domain between -1 and +1.
The range of the arcsine function is the set of all possible values that the function can output. Since the sine function has a range between -1 and +1, the arcsine function will have a range between -π/2 and +π/2.
Therefore, the range of y = Arc sin x is -π/2 ≤ y ≤ π/2.