A=\frac12r^2\theta (\theta in radians)

30^{\circ}, 45^{\circ}, 60^{\circ} in radians?

\frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}

Definition of one radian?

The angle subtended at the centre by an arc equal in length to the radius.

Why check calculator mode?

Trig functions of a radian angle are wrong in degree mode.

Radian measure, arc length and sector areaEdexcel International A Level Maths: Flashcards

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How many degrees is $\pi$ radians?

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How many degrees is $\pi$ radians?: $180^{\circ}$
Convert degrees to radians?: Multiply by $\frac{\pi}{180}$ .
Convert radians to degrees?: Multiply by $\frac{180}{\pi}$ .
Arc length formula?: $s=r\theta$ ( $\theta$ in radians)
Sector area formula?: $A=\frac12r^2\theta$ ( $\theta$ in radians)
Another form of the sector area?: $A=\frac12rs$
Perimeter of a sector?: $2r+r\theta$
$30^{\circ}$ , $45^{\circ}$ , $60^{\circ}$ in radians?: $\frac{\pi}{6}$ , $\frac{\pi}{4}$ , $\frac{\pi}{3}$
$90^{\circ}$ and $360^{\circ}$ in radians?: $\frac{\pi}{2}$ and $2\pi$
Definition of one radian?: The angle subtended at the centre by an arc equal in length to the radius.
How do you find $\theta$ from $s$ and $r$ ?: $\theta=\frac{s}{r}$
Area of the minor segment?: $\frac12r^2(\theta-\sin\theta)$
Why check calculator mode?: Trig functions of a radian angle are wrong in degree mode.

Exam questions on Radian measure, arc length and sector area

A sector $OAB$ of a circle with centre $O$ and radius $6$ cm has angle $\frac{2\pi}{3}$ radians at $O$ .
Find the perimeter of the sector $OAB$ , giving your answer in the form $a+b\pi$ .2 marks
A circle has radius $8$ cm. A sector of this circle has an arc of length $10$ cm.
Give the angle of the sector in degrees, correct to 1 decimal place.2 marks
A sector $OPQ$ of a circle with centre $O$ and radius $9$ cm has area $36$ cm $^2$ .
Find the angle $POQ$ in radians.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).