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5.05 Circular functions: sine and cosine

Interactive practice questions

Consider the equation $y=\sin x$y=sinx.

a

Using the fact that $\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$sinπ3=32, what is the value of $\sin\frac{2\pi}{3}$sin2π3?

b

Using the fact that $\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$sinπ3=32, what is the value of $\sin\frac{4\pi}{3}$sin4π3?

c

Using the fact that $\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$sinπ3=32, what is the value of $\sin\frac{5\pi}{3}$sin5π3?

d

Complete the table of values. Give your answers in exact form.

$x$x $0$0 $\frac{\pi}{3}$π3 $\frac{\pi}{2}$π2 $\frac{2\pi}{3}$2π3 $\pi$π $\frac{4\pi}{3}$4π3 $\frac{3\pi}{2}$3π2 $\frac{5\pi}{3}$5π3 $2\pi$2π
$\sin x$sinx $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
e

Draw the graph of $y=\sin x$y=sinx.

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Easy
6min

Consider the equation $y=\cos x$y=cosx.

Easy
5min

Consider the graph of $y=\sin x$y=sinx given below.

Easy
1min

Consider the graph of $y=\cos x$y=cosx given below.

Easy
< 1min
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Outcomes

ACMMM034

understand the unit circle definition of cos⁡θ, sin⁡θ and tan⁡θ and periodicity using radians

ACMMM036

recognise the graphs of y=sin⁡x, y=cos⁡x, and y=tan⁡x on extended domains

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