The function $f(x)$ is defined by

where $x$ is measured in radians.

1. Express $f(x)$ in the form

   $$R\cos (x-\alpha )$$

   where $R>0$ and $\alpha$ is an acute angle measured in radians.

2. Hence, show that

   $$2-f\left(\frac{3\pi }{8}\right)\approx \frac{{\pi }^2}{576}$$

Part (a) requires you to put $f(x)$ in harmonic form

For part (b), $\frac{3\pi }{8}$ cannot be considered small, so we can't use the small angle approximation directly. Try using the harmonic form of $f(x)$ that you got in part (b).