Is the derivative of a sinusodial function a sinusodial function?

Question

help

Answer 1

nop. it is a cosinusoidal

Answer 2

Yes. The term "sinusoidal" is broad enough to encompass sin or cos of x or constants times x, and constant multiples of those functions.

And the derivative of any such function is another such function.

The same holds true if the term is used so broadly that the sum of sinusoidal functions is itself sinusoidal.

Answer 3

sort of, the derivative of sin(x) is cos(x). The derivative is the rate of change on a graph, so plot a sighn function, and where it increases represents a positive trace on the derivative graph, and where it decreases represents a negative trace on the derivative graph

Answer 4

That is mostly correct. Here's how it works:

The derivative of sin(x) is cos(x).
The derivative of cos(x) is -sin(x).
The derivative of -sin(x) is -cos(x).
The derivative of -cos(x) is sin(x).

All derivatives are taken with respect to x.

If you take four derivatives of a simple sine function, you will end up back where you started. However, if you're taking derivatives of sin(k*x), where k is some constant, you won't end up back where you started after four derivatives. Instead, you'll end up with k^4*sin(k*x).

Answer 5

Yes.

d/dx(sinx) = cosx

d/dx(cosx) = -sinx