Everything from the 2 lessons of this topic on a few pages: the key idea of each lesson, the diagram to remember, the points to learn and the traps examiners set. Read it, cover it, test yourself.
One radian is the angle at the centre of a circle subtended by an arc equal in length to the radius. A full turn is \(2\pi\) radians, so \(\pi \text{ rad} = 180^\circ\): multiply by \(\dfrac{\pi}{180}\) to go from degrees to radians, and by \(\dfrac{180}{\pi}\) to go back.
Your calculator must be in the right mode. \(\sin 1.2\) in degree mode gives \(0.0209\) instead of \(0.932\). If a question gives angles in radians (or uses \(\pi\)), switch to radian mode before pressing anything.
Do not multiply \(\dfrac{7\pi}{12}\) by 180 and stop: that gives \(105\pi\), not \(105^\circ\). The \(\pi\) in the angle cancels with the \(\pi\) in \(\dfrac{180}{\pi}\).
Never mix units in an angle sum. If two angles are \(\dfrac{\pi}{4}\) and \(1.1\), the third is \(\pi - \dfrac{\pi}{4} - 1.1\), not \(180 - \dfrac{\pi}{4} - 1.1\).
For a sector of radius \(r\) and angle \(\theta\) radians: arc length \(s = r\theta\) and area \(A = \tfrac{1}{2}r^2\theta\). A segment is a sector minus a triangle, so its area is \(\tfrac{1}{2}r^2\theta - \tfrac{1}{2}r^2\sin\theta\), and its chord is \(2r\sin\dfrac{\theta}{2}\).
\(s = r\theta\) only works with \(\theta\) in radians. If the angle is given as \(60^\circ\), convert it to \(\dfrac{\pi}{3}\) first; \(9 \times 60 = 540\) cm is nonsense.
Forgetting the \(\tfrac{1}{2}\) doubles the answer. A useful check: the sector must be smaller than the whole circle, \(\pi r^2\).
The triangle in a segment has area \(\tfrac{1}{2}r^2\sin\theta\), using the angle at the centre, not \(\tfrac{1}{2} \times\) chord \(\times r\). And in a perimeter, use the straight chord, not another arc.