Are sine and cosine functions bounded?

In the case of sin x and cos x, since they are both bounded and periodic, we can talk about their amplitude, the largest value that | sin x| and | cos x| can take, or, equivalently, the largest vertical distance the points on the graphs of these two functions can get from the x-axis.

What are Cos and sin bounded?

as y → ±∞. These imply that the sine and cosine are bounded on the real x-axis, but unbounded on the imaginary y-axis.

Is the sine function bounded?

Thus Sin x is a bounded function. There can be infinite m and M. Minimum value of sinx is -1 and maximum value is 1.

Which trig functions are bounded?

1. Known boundedness. We know that some functions – notably some elementary functions – are bounded, for instance all constant functions, sine, cosine, and all inverse trig functions.

What makes a function bounded?

A function f(x) is bounded if there are numbers m and M such that m≤f(x)≤M for all x . In other words, there are horizontal lines the graph of y=f(x) never gets above or below.

Can a function be bounded but not continuous?

A function is bounded if the range of the function is a bounded set of R. A continuous function is not necessarily bounded. For example, f(x)=1/x with A = (0,∞). But it is bounded on [1,∞).

How do you determine if a function is bounded or unbounded?

A function that is not bounded is said to be unbounded. If f is real-valued and f(x) ≤ A for all x in X, then the function is said to be bounded (from) above by A. If f(x) ≥ B for all x in X, then the function is said to be bounded (from) below by B.

Why continuous function is bounded?

By the boundedness theorem, every continuous function on a closed interval, such as f : [0, 1] → R, is bounded. All complex-valued functions f : C → C which are entire are either unbounded or constant as a consequence of Liouville’s theorem. In particular, the complex sin : C → C must be unbounded since it is entire.

What functions are bounded below?

Today in Pre-Calculus. Definition: A function f is bounded below if there is some number b that is less than or equal to every number in the range of f. Any such number b is called a lower bound of f.