New Zealand
Level 7 - NCEA Level 2

# Key features of sine and cosine curves

## Interactive practice questions

The value of $\sin\theta$sinθ can be represented on the $xy$xy-plane below. Consider the curve $y=\sin\theta$y=sinθ and answer the following questions.

a

Fill in the gaps below.

A rotation of $390^\circ$390° has the same rotation as the acute angle with measure $\editable{}$$^{\circ}. So \sin390^\circsin390°==\sin\editable{}sin. A rotation of 480^\circ480° has the same rotation as the obtuse angle with measure \editable{}$$^{\circ}$.

So $\sin480^\circ$sin480°$=$=$\sin\editable{}$sin.

A rotation of $570^\circ$570° has the same rotation as the reflex angle with measure $\editable{}$$^{\circ}$.

So $\sin570^\circ=\sin210^\circ$sin570°=sin210°.

b

Here is the graph of $y=\sin\theta$y=sinθ for $0\le\theta\le720^\circ$0θ720°.

What do you notice about the nature of $y=\sin\theta$y=sinθ?

The function values and shape of the graph repeat at regular intervals.

A

The function values and shape of the graph repeat at irregular intervals.

B

The function values and shape of the graph repeat at regular intervals.

A

The function values and shape of the graph repeat at irregular intervals.

B
c

The number of degrees it takes for the curve to complete a full cycle is called the period of the function.

Determine the period of $y=\sin\theta$y=sinθ.

Easy
Approx 3 minutes

Consider the curve $y=\sin x$y=sinx drawn below and answer the following questions.

Consider the curve $y=\cos x$y=cosx drawn below and answer the following questions.

Consider the curve $y=\sin x$y=sinx drawn below and determine whether the following statements are true or false.

### Outcomes

#### M7-2

Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

#### 91257

Apply graphical methods in solving problems