NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Intro to sin(x), cos(x) and tan(x)

## Interactive practice questions

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

a

Using the fact that $\sin\frac{\pi}{6}=\frac{1}{2}$sinπ6=12, what is the value of $\sin\frac{5\pi}{6}$sin5π6?

b

Using the fact that $\sin\frac{\pi}{6}=\frac{1}{2}$sinπ6=12, what is the value of $\sin\frac{7\pi}{6}$sin7π6?

c

Using the fact that $\sin\frac{\pi}{6}=\frac{1}{2}$sinπ6=12, what is the value of $\sin\frac{11\pi}{6}$sin11π6?

d

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

 $x$x $\sin x$sinx $0$0 $\frac{\pi}{6}$π6​ $\frac{\pi}{2}$π2​ $\frac{5\pi}{6}$5π6​ $\pi$π $\frac{7\pi}{6}$7π6​ $\frac{3\pi}{2}$3π2​ $\frac{11\pi}{6}$11π6​ $2\pi$2π $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
e

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

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Easy
Approx 6 minutes
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Consider the equation $y=\cos x$y=cosx.

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

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

### Outcomes

#### M8-2

Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions