The small angle approximation is often made to simplify derivations and calculations.

The small angle approximation is often made to simplify derivations and calculations. For the following angles ?, compare the true value of the sine of the angle to the to the small angle approximation (using only the first term in the series expansion of the sine) by determining the fractional error (let the fractional error be positive). NOTE: If you explicitly use &pi (pi); to convert from degrees to radians, use an accurate value for &pi (pi);.

DIGRESSION: The fractional error is the difference between the approximate or measured value and the "known or true" value divided by the known or true value. The percent error is the fractional error expressed in percent (percent error = 100% × fractional error). When we are comparing two experimental values, we often have no reason to think that one is "better" than the other. In these cases, we can compare them by calculating the fractional difference, which is the difference divided by their average. The percent difference is the fractional difference expressed as in percent (percent difference = 100% × fractional difference).
Note: we are asking for the fractional error in the sine value, not the percentage error.

a) ? = 1.55°:
Fractional Error =

b) ? = 5.68°:
Fractional Error =
c) ? = 16.78°:
Fractional Error =
d) ? = 43.66°:
Fractional Error =

You can set up a spreadsheet to do this easily.
A1. theta * pi()/180 is the angle in radians
A2. =sin(a1)
a3 =(a1-a2)/(A1+a2) /2

errors are 3.0*10^-5 , 0.00041, 0.0036, and 0.025 for your four angles.