Perimeter of a sector?

2r+r\theta (two radii plus the arc)

\frac12r^2(\theta-\sin\theta): sector minus triangle

Why is \tan\frac{\pi}{2} undefined?

\cos\frac{\pi}{2}=0, so \frac{\sin}{\cos} divides by zero

Exact value of \cos\frac{2\pi}{3}?

-\frac12 (related angle \frac{\pi}{3}, cosine negative in quadrant 2)

Exact value of \sin\frac{7\pi}{6}?

-\frac12 (related angle \frac{\pi}{6}, sine negative in quadrant 3)

Radian measure, arc length and exact valuesEdexcel A-Level Maths: Flashcards

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Question

How many radians in $180^\circ$?

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How many radians in $180^\circ$ ?: $\pi$ radians
Convert $\frac{5\pi}{6}$ radians to degrees.: $150^\circ$
Arc length formula in radians?: $s=r\theta$
Sector area formula in radians?: $A=\frac12r^2\theta$
Perimeter of a sector?: $2r+r\theta$ (two radii plus the arc)
Area of a segment?: $\frac12r^2(\theta-\sin\theta)$ : sector minus triangle
$\sin\frac{\pi}{6}$ and $\cos\frac{\pi}{6}$ ?: $\frac12$ and $\frac{\sqrt3}{2}$
$\sin\frac{\pi}{4}$ and $\cos\frac{\pi}{4}$ ?: Both $\frac{\sqrt2}{2}$
$\sin\frac{\pi}{3}$ and $\cos\frac{\pi}{3}$ ?: $\frac{\sqrt3}{2}$ and $\frac12$
Exact values of $\tan\frac{\pi}{6}$ , $\tan\frac{\pi}{4}$ , $\tan\frac{\pi}{3}$ ?: $\frac{\sqrt3}{3}$ , $1$ , $\sqrt3$
Why is $\tan\frac{\pi}{2}$ undefined?: $\cos\frac{\pi}{2}=0$ , so $\frac{\sin}{\cos}$ divides by zero
Exact value of $\cos\frac{2\pi}{3}$ ?: $-\frac12$ (related angle $\frac{\pi}{3}$ , cosine negative in quadrant 2)
Exact value of $\sin\frac{7\pi}{6}$ ?: $-\frac12$ (related angle $\frac{\pi}{6}$ , sine negative in quadrant 3)

Exam questions on Radian measure, arc length and exact values

A sector $OAB$ of a circle has centre $O$ , radius $6$ cm and angle $AOB=\frac{2\pi}{3}$ radians.
Find the exact perimeter of the sector $OAB$ .2 marks
Consider the angle $\theta=\frac{5\pi}{6}$ radians, which lies in the second quadrant.
Hence show that $\tan\theta=-\frac{\sqrt3}{3}$ .2 marks
A sector of a circle of radius $5$ cm has perimeter $16$ cm. The angle of the sector is $\theta$ radians.
Find the value of $\theta$ .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).