## Calculus (3rd Edition)

$$\kappa(x) =\frac{|\cos x|}{\left(1+\sin^2 x\right)^{3 / 2}}, \quad \kappa(0)= 1.$$
We have $$\kappa(x)=\frac{\left|f^{\prime \prime}(x)\right|}{\left(1+f^{\prime}(x)^{2}\right)^{3 / 2}}=\frac{|\cos x|}{\left(1+\sin^2 x\right)^{3 / 2}},$$ and hence $$\kappa(0)=\frac{|\cos 0|}{\left(1+\sin^20\right)^{3 / 2}}=1.$$