If understood your question correctly, this is what you are trying to do:
t = 0:.1:3; % Time
Data = exp(2*cos(t)); % Data vector
rng(1) % For this demo reproducibility purposes
ts = rand(1); % Wave starts at a time point
dt = 0.05; % Wave collected at a time step
tend = 5*rand(1); % Wave data collection ends at this time
tpoints = ts:dt:tend; % Specific time points at which the wave data was collected
Wave = sin(2*tpoints); % Wave Data vector
plot(t, Data, 'r--', 'DisplayName', 'Data with time')
hold on
plot(tpoints, Wave, 'bo-.', 'DisplayName', 'Wave with specific time points')
legend('Show')
xlabel('Time, [s]')
ylabel('Data & Wave')
grid on
