# What are the maximum and minimum values of the sine function?

2. 3. Because the sine function has a range of -1 to 1, the minimum is -1 and the maximum is 1. 4. The sine function has an infinite range. It is defined for all real numbers except 0.

## What is the minimum value that the graph of y sin x assumes?

The graph of y = sinx is included here.

## What is the maximum value of y sin x?

When x = p2+2np, where n is an integer, the maximum value of y = sin (x) occurs. When x = 3p2+2np, where n is an integer, y = sin (x) has the smallest value. The value of y is 1/sqrt(3).

In particular, when x = 2p2+2np, where n is an integer, then y = sin (x) = 1/sqrt(3).

Thus, the maximum value of y sin (x) is 1/sqrt(3) when x = 2p2+2np, where n is an integer.

## What is the restricted domain for the sine function?

Because the limited sine function satisfies the horizontal line test, it is one to one. Each value in the range (-1 to 1) is within the restricted domain (p/2, p/2). A division by zero would also cause problems for the sin function.

## What is the maximum value of f in the interval?

The function values at the interval's endpoints are f(0) = 1 and f(2p) = 1, meaning that f(x) has a maximum function value at x = p/4 and a minimum function value at x = 5p/4. It is worth noting that in this case, the maximum and minimum occur at important parts in the function. If we looked only at the sign of the derivative, then we would not be able to say anything about where the maximum or minimum might be located.

In general, if there are multiple points at which the function value is a maximum or minimum, then they will all be important in determining the location of these extrema. It is possible that some may be more important than others, but it is impossible to say something about which ones are most important without looking at the function in detail. In many cases, you can tell that there is going to be one point of interest near each endpoint, but beyond that, all bets are off. There are examples of functions for which all points are important, but they are very rare.

It is also possible that there might be locations inside the interval where the function value is constant (or varies linearly). If this is the case, then we could say that there is no point where the function value is a maximum or minimum because it cannot change direction inside the interval.

Finally, there are functions for which none of the points above are important.

## What is the range for sine?

The sine function has a range of [-1, 1]. The tangent function has a period of p, whereas sine and cosine have periods of 2 p. Therefore, the range of tan can be from 0 to p while the range of sin and cos are both between -1 and 1.

## Is sin theta greater than 1?

No, Sin's value ranges between -1 and 1, hence it can never be more than 1. In fact, it is less than 1 when plotted on a graph.

## What is the maximum and minimum value of sin 2 theta?

Sin22nd has a maximum value of one. Because if you were to draw a picture of a right angle on a piece of paper, it would look like this:

This means that any number less than or equal to one is an acceptable answer for this question.

The minimum value of sin 22nd is zero. This can be seen in the graph below. The area under the curve is zero, so the smallest possible value of sin 22nd is zero:

Because zero times anything is still zero, this means that cosine is always returning true or false depending on whether its argument is less than or equal to zero. If so, then the product is also less than or equal to zero; otherwise, it's greater than zero.

That means that for any number less than or equal to zero, the expression (sin x) will always return true.

##### Max Rose

Max Rose is an educator and writer. He loves to help people understand complex topics in easy to understand ways. He also enjoys sharing his own personal stories about what it's like being an educator in this field.