Circular measure — common mistakes

Always check your calculator mode! For circular measure problems, it must be in Radians (RAD). A common error is calculating $\sin\theta$ with the calculator in Degrees (DEG) mode, which will give an incorrect answer for the area of the triangle and segment.

Degrees are arbitrary (360 is just a convenient number with many factors). Radians are intrinsic to the circle, defining an angle by the ratio of arc length to radius. This 'natural' unit makes calculus involving trigonometric functions much, much simpler. For example, the derivative of sin(x) is cos(x) only when x is in radians.

Yes, and you often should! If a question asks for an 'exact answer', it almost always means you should leave $\pi$ in your answer rather than using a decimal approximation like 3.14159. For example, $\frac{16\pi}{3}$ is an exact answer.

Think of a pizza. A 'sector' is a full slice, from the centre to the crust, bounded by two radii and an arc. A 'segment' is just the 'crust-end' of the slice, the part bounded by the straight-line chord and the curved arc.

Make it a habit. Before starting any question involving trigonometry or circles in A-Level Maths, physically check your calculator's mode. Most P1 circular measure questions will require RAD mode. It's a simple check that saves many marks.