Chapter 4 - Applications of the Derivative - 4.4 The Shape of a Graph - Exercises - Page 194: 7

Concave upwards for all $\theta$ in (0,$\pi$) and concave down for all $\theta$ in ($\pi, 2\pi$). The point of inflection is at $\theta=\pi$.

$y=f(\theta)=\theta-2\sin \theta$ $f'(\theta)=1-2\cos\theta$ $f''(\theta)=-2\times-\sin\theta=2\sin\theta$ $f''(\theta)$ is positive when $\theta\in(0,\pi)$ and is negative when $\theta\in (\pi,2\pi)$.