Why is the graph of sine a curve?

When the sine of an angle is plotted against that angle measure, the result is a classic “sine curve” shape. To graph the sine function, we mark the angle along the horizontal x axis, and for each angle, we put the sine of that angle on the vertical y-axis.

Is sine function smooth?

The graph of sine function is smooth because it is defined for all real values of x and it is differentiable at every x.

What does it mean if a function is smooth?

A smooth function is a function that has continuous derivatives up to some desired order over some domain.

What does it mean for a curve to be smooth?

A smooth curve is a curve which is a smooth function, where the word “curve” is interpreted in the analytic geometry context. In particular, a smooth curve is a continuous map from a one-dimensional space to an. -dimensional space which on its domain has continuous derivatives up to a desired order.

Is a sine graph a function?

The sine and cosine functions have several distinct characteristics: They are periodic functions with a period of 2π. The domain of each function is (−∞,∞) and the range is [−1,1]. The graph of y = sin x is symmetric about the origin, because it is an odd function.

What is a function that is smooth but not continuous?

For a function to be smooth, it has to have continuous derivatives up to a certain order, say k. We say that function is Ck smooth. An example of a continuous but not smooth function is the absolute value, which is continuous everywhere but not differentiable everywhere.

What graph is a smooth curve?

Smooth line graph is a graph that is drawn by hand. Bit like the one shown in the picture above. Notice how the curve is smooth and not jagged. Asmooth curve is a continuous map from a one-dimensional space to an -dimensional space which on its domain has continuous derivatives up to a desired order.

What is a smooth curve graph used for?

If you are plotting measured data, the only valid connecting curve between points is a straight line (or a line which is fitted to a function that comes from a physical model of the data). A smoothed curve implies that the data goes places where it has not been measured.

How does sine function work?

In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse. In any right triangle, the sine of an angle x is the length of the opposite side (O) divided by the length of the hypotenuse (H).