Get t co-ordinate based off y co-ordinate

I am trying to get the t co-ordinate of the following graph when y = 40

t = 0 * pi:0.119:4 * pi;

a = 57;

phase_angle = 0.26;

y = a*sin((67*pi*t) + phase_angle);

plot(t,y);

so i want the co-ordinate (t, 40)

how can I get t?

Thanks

Answer 1

[Star Strider]

Try these:

t = 0 * pi:0.119:4 * pi;
a = 57;
phase_angle = 0.26;
y = a*sin((67*pi*t) + phase_angle);

y_ofst = y-40;
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Approximate Zero-Crossing Indices Of Argument Vector
y40 = zci(y_ofst);

for k = 1:numel(y40)
    idxrng = y40(k)+[-1,1]
    B = [t(idxrng); ones(size(t(idxrng)))].' \ y_ofst(idxrng).'         % Linear Regression
    xxct(k) = -B(2)/B(1)
end

figure
plot(t,y,   xxct,40+[0 0],'pg')

alternatively:

for k = 1:numel(y40)
    idxrng = y40(k)+[-1,1]
    xxct(k) = interp1(y(idxrng), t(idxrng), 40)                         % Interpolation
end

figure
plot(t,y,   xxct,40+[0 0],'pg')

Choose the most appropriate option for your application. Both give the same result.