= Solution
At the central values, $z=\sqrt{\tan45^\circ}+0.10^2=1.010$. For independent input standard errors, linear propagation gives
$$
\sigma_z^2=\left(\frac{\sec^2x}{2\sqrt{\tan x}}\sigma_x\right)^2+(2y\sigma_y)^2.
$$
The angular derivative here is with respect to radians, so $\sigma_x=2\pi/180=0.03491$. At $x=\pi/4$, the derivative is one, and
$$
\sigma_z=\sqrt{(0.03491)^2+(0.2\times0.02)^2}=0.0351.
$$
Thus \b[$\boxed{z=1.010\pm0.035}$], with the stated <measurement uncertainty> interpreted as one <standard error>. Correlated inputs would require a <covariance> term; their correlation is not supplied.
Back to article page
