Figure 4 shows the relative errors using the power series.

Each relative error number is an average over all the 366 data points.

The relative error in the angle is then about 17 percent.

There are two features of relative error that should be kept in mind.

In the figure the relative error is shown, following the expected scaling.

This value is the biggest possible numerator for the relative error.

An additional adjustment can be added to reduce the maximum relative error.

Figure 3 shows the relative errors of the small angle approximations.

Does this compression effect (or the relative error) increase with larger ratios?

The percent error is the relative error expressed in terms of per 100.

The first graph in this section shows the relative error vs. n, for 1 through all 5 terms listed above.

This gives us a relative error of 1.

All these numbers round to with relative error .

The relative error of this approximation does not exceed .

The relative error in spiking experiments (28%) suggests that there is room for future improvement.

The angles at which the relative error exceeds 1% are as follows:

The same relative error occurs in each calculation.

The relative error in T is larger than might be reasonable so that the effect of the bias can be more clearly seen.

One commonly distinguishes between the relative error and the absolute error.

The relative error is the absolute error divided by the magnitude of the exact value.

Uncertainties can also be defined by the relative error (Δx)/x, which is usually written as a percentage.

The relative error of the approximation decays exponentially for large .

The simulation shows the observed relative error in g to be about 0.011, which demonstrates that the angle uncertainty calculations are correct.

He also gave the following approximation formula for sin(x), which had a relative error of less than 1.9%:

The following shows the approximations and their absolute and relative errors for both methods of approximation.