How to find x value for a known Y in array?

I have x and y arrays for a sine wave. I am trying to find the x value for when y is equal to 0, since the y array does not contain a value of 0. How can I do so?

Answer 1

[Torsten]

x = 0.1:0.1:4*pi-0.1;
y = sin(x);
i = find(y(1:end-1).*y(2:end) <= 0)

i = 1×3

31 62 94

x_root = x(i)-y(i).*(x(i+1)-x(i))./(y(i+1)-y(i))

x_root = 1×3

3.1416 6.2832 9.4248

[pi,2*pi,3*pi]

ans = 1×3

3.1416 6.2832 9.4248

[Zeyad Elreedy]

Thanks, but can I have some explanation? I don't quite get what's happening. I have also seen some answers mentioning using interp1(). Would this be valid in this case?

[John D'Errico]

@Zeyad Elreedy

You cannot use interp1 on a function where there would be multiple solutions. A sine wave is a perfect example of a case where that fails. The inverse relation there is multi-valued.

What @Torsten did was to find a pair of points that bracket a solution, then use a linear reverse interpolation, valid locally.

[Torsten]

I determine x(i) and x(i+1) between which y changes sign. Then I approximate the zero between x(i) and x(i+1) by linear interpolating between the points (x(i),y(i)) and (x(i+1),y(i+1)) and determining the x_root value as the x-value where this line crosses the x-axis.

So interp1 is implicitly used in the line

x_root = x(i)-y(i).*(x(i+1)-x(i))./(y(i+1)-y(i))

[Zeyad Elreedy]

I understand now. Thanks a lot!