Cosine tuning is ubiquitous in the motor system, yet a satisfying explanation of its origin is lacking. Here we argue that cosine tuning minimizes expected errors in force production, which makes it a natural choice for activating muscles and neurons in the final stages of motor processing. Our results are based on the empirically observed scaling of neuromotor noise, whose standard deviation is a linear function of the mean. Such scaling predicts a reduction of net force errors when redundant actuators pull in the same direction. We confirm this prediction by comparing forces produced with one versus two hands and generalize it across directions. Under the resulting neuromotor noise model, we prove that the optimal activation profile is a (possibly truncated) cosine--for arbitrary dimensionality of the workspace, distribution of force directions, correlated or uncorrelated noise, with or without a separate cocontraction command. The model predicts a negative force bias, truncated cosine tuning at low muscle cocontraction levels, and misalignment of preferred directions and lines of action for nonuniform muscle distributions. All predictions are supported by experimental data.