New Zealand
Level 8 - NCEA Level 3

# Symmetrical and periodic nature of trig functions

## Interactive practice questions

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

a

How long is one cycle of the graph?

b

State the $x$x values for which $\sin x=0$sinx=0, from $x=0$x=0 to $x=2\pi$x=2π inclusive.

c

State the first $x$x value for which $\sin x=0.5$sinx=0.5

d

Using the symmetry of the graph, for what other value of $x$x shown on the graph does $\sin x=0.5$sinx=0.5?

e

Using the symmetry of the graph, for what values of $x$x does $\sin x=-0.5$sinx=0.5?

Easy
Approx 6 minutes

Examine the graph of $y=\cos x$y=cosx.

Examine the graph of $y=\tan x$y=tanx.

Examine the graph of $y=\sin x+3$y=sinx+3.

### Outcomes

#### M8-2

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