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1.04 Trigonometric functions

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 equation $y=\tan x$y=tanx.

Easy
4min

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

Easy
1min
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Outcomes

3.1.6

use trigonometric functions and their derivatives to solve practical problems

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