= Solution
Treat the repeated angles as independent measurements of one fixed angle. Their <sample mean>, sample <standard deviation> and <standard error> of the <mean> are
$$
\bar\theta=31.24^\circ,\qquad s_\theta=1.997^\circ,\qquad
\sigma_{\bar\theta}=s_\theta/\sqrt5=0.8931^\circ=0.01559\,\mathrm{rad}.
$$
For $y=A\cos\theta$, uncorrelated <standard uncertainties> give
$$
\left(\frac{\sigma_y}{|y|}\right)^2
=\left(\frac{\sigma_A}A\right)^2+\tan^2\bar\theta\,\sigma_{\bar\theta}^2.
$$
Interpreting the stated 1% <amplitude> accuracy as a <standard uncertainty>,
$$
\boxed{\sigma_y/|y|=0.01376\simeq1.38\%.}
$$
Use radians in the derivative. This is uncertainty in the result using the <mean> angle, not the spread of individual angle measurements; the latter convention would use $s_\theta$ and give about $2.34\%$. An accuracy bound or systematic angular calibration error would require a different uncertainty model.
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