= Solution
At $x=10\delta_D$, the daily component is multiplied by $e^{-10}\simeq4.54\times10^{-5}$ and has a lag of ten radians. The annual component instead has $x/\delta_Y=10/\sqrt{365}\simeq0.5234$. Hence
$$
\boxed{\begin{aligned}
\Theta-\Theta_0={}&A e^{-10/\sqrt{365}}\cos(\omega_Yt-10/\sqrt{365})\\
&+B e^{-10}\cos(\omega_Dt-10).
\end{aligned}}
$$
The sketch is nearly a smooth annual sinusoid, with annual <amplitude> \b[about $0.5925A$] and annual <phase lag> \b[about $0.5234$ radians], corresponding to about $30.4$ days on the chosen year scale. The tiny daily component is retained in the formula rather than declared identically zero.
Back to article page
