[throwaway744678]

Here are the graphs [0] for both functions from the article:

+ 1/2 * sin(x * pi / 2)

+ 0.785313 * x - 0.321615 x^3 + 0.0363551 x^5

[0] https://www.desmos.com/calculator/x7tm7i2qtj

[hexomancer]

Also here is the same graph with the classic taylor expansion of sin with 3 terms (x + (x^3)/(3!) + (x^5)/(5!)):

https://www.desmos.com/calculator/emfz64hjhv

[jacobolus]

Showing relative error: https://www.desmos.com/calculator/a3whptxkqu