Smooth strictly positive sine function

[quarkz]

Hi,

Is there a function which is very similar to a sine function, except that it's strictly positive ie the negative part of the sine function is reflected along the x axis? It must also be varying smoothly.

To get a strictly positive sine function, I can just use abs(sin(x)), abs = absolute. But then there's a non-smooth sudden change.

Another way is to use (sin(x))^2, but the entire function is now much sharper. I just want it to be different from the original sine function at the non-smooth part.

Thanks!

 

[pka]

Hi,

Is there a function which is very similar to a sine function, except that it's strictly positive ie the negative part of the sine function is reflected along the x axis? It must also be varying smoothly.

To get a strictly positive sine function, I can just use abs(sin(x)), abs = absolute. But then there's a non-smooth sudden change.

Another way is to use (sin(x))^2, but the entire function is now much sharper. I just want it to be different from the original sine function at the non-smooth part.

$\displaystyle f(x)=\sin(x)+1$ See the graph.

 

[Quaid]

it's strictly positive ie the negative part of the sine function is reflected along the x axis

To get a strictly positive sine function, I can just use abs(sin(x))

Another way is to use (sin(x))^2

Hi quarkz:

Each of the three descriptions above lead to a function that outputs zero, whenever its input is a multiple of Pi.

Zero is not a positive number, so none of those describe a strictly-positive function.

If you shift the graph of sin(x) vertically upward, by adding a constant greater than 1, then the entire graph will lie above the x-axis, and the result will be a function whose outputs are strictly-positive numbers.

Cheers :smile: