Why is there a restriction on arcsin?

The domain of sin(x) comprises all angles up to infinity, but the range of Arcsin(x) is restricted to a representative class in the interval [0,2π), wherby if θ is a solution, so then is θ±2kπ.

What quadrants is the arcsin function restricted to?

Correct answer: The sine function is negative in quadrants III and IV, so arcsin (−½) could fall in either of these quadrants. The below image shows where each function is positive. Any that are not noted are negative. Since sine is positive in Quadrants I and II, it is negative in Quadrants III and IV.

What are the restrictions for arcsin?

Domain and range: The domain of the arcsine function is from −1 to +1 inclusive and the range is from −π/2 to π/2 radians inclusive (or from −90° to 90°). The arcsine function can be extended to the complex numbers, in which case the domain is all complex numbers.

Why does arcsin only have one answer?

In summary, there are infinitely many x such that sinx=12, but arcsin is a function so it can only give one of them back. arcsin12 is therefore just A solution to the equation, not ALL solutions. Since the sine function is not one-to-one, the sine function does not have an inverse.

Why is the domain of arcsin?

The domain of arcsinx is the interval [−1,1] and it is undefined elsewhere. Within this domain it has range [−π2,π2], and these values as input to sinx produce values in the range [−1,1]. So the graph will look like y=x restricted to the domain −1≤x≤1, which is Graph E.

What is the difference between arcsin and sin 1?

arcsin(x) is the inverse to the function sin(x). For a function to have an inverse, it first must be a function and thus every input must determine only one distinct output. Second, it must be one-to-one on its domain, or every output correlates to exactly one input. Looking at the graph of f(x)=sin(x):

Why is arcsin not a function?

This function is one-to-one and onto and therefore has an inverse. Its inverse is commonly denoted sin−1 or arcsin. Notice however that this terminology is not strictly accurate: arcsin is not the inverse of sin, it is the inverse of f, which is a different function.

Which restricted domain would allow you to define the inverse cosine function?

To define the inverse functions for sine and cosine, the domains of these functions are restricted. The restriction that is placed on the domain values of the cosine function is 0 ≤ x ≤ π (see Figure 2 ). This restricted function is called Cosine.

Is arcsin the same as sin 1?

Strictly speaking, the symbol sin-1( ) or Arcsin( ) is used for the Arcsine function, the function that undoes the sine. Arcsine may be thought of as “the angle whose sine is” making arcsine(1/2) mean “the angle whose sine is 1/2” or /6.

Can arcsin have two answers?

Are sin 1 and arcsin the same thing?

It represents the inverse of the sine function. Recall f(x) and f-1(x). sin-1x means the same as arcsin x, i.e., the arc whose sine is x.

What is the range of the function y = arcsin x?

The angle whose sine is − x is simply the negative of the angle whose sine is x. arcsin (−½) = −arcsin (½) = −. The range, then, of the function y = arcsin x will be angles that fall in the 1st and 4th quadrants, between − and. Angles whose sines are positive will be 1st quadrant angles.

What is the value of arcsin in the first quadrant?

Now, Let us assume the value arcsin is not limited to the first quadrant. If you find out the arcsin, arcsin(0) can be either 0 or pi. arcsin(1/2) can be either pi/6 or 5pi/6. arcsin(1/sqrt(2)) can be either pi/4 or 3pi/4.

Why is arcsin(3) undefined?

arcsin (3) is undefined because 3 is not within the interval -1≤arcsin (θ)≤1, the domain of arcsin (x). Generally, functions and their inverses exhibit the relationship f (f -1 (x)) = x and f -1 (f (x)) = x given that x is in the domain of the function.

What is the arcsecant of the cosine function?

The arcsecant function takes a trigonometric ratio on the unit circle as its input and results in an angle measure as its output. and is the angle measure which, when applied to the cosine function , results in .