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Stage 5.1-3

10.02 Graphs of trigonometric functions

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 $380^\circ$380° has the same rotation as the acute angle with measure $\editable{}$$^{\circ}$.

So $\sin380^\circ$sin380°$=$=$\sin\editable{}$sin.

A rotation of $480^\circ$480° has the same rotation as the obtuse angle with measure $\editable{}$$^{\circ}$.

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

A rotation of $580^\circ$580° has the same rotation as the reflex angle with measure $\editable{}$$^{\circ}$.

So $\sin580^\circ=\sin220^\circ$sin580°=sin220°.

b

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

Loading Graph...

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
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
2min

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

Easy
< 1min

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

Easy
< 1min

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

Easy
< 1min
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Outcomes

MA5.3-15MG

applies Pythagoras' theorem, trigonometric relationships, the sine rule, the cosine rule and the area rule to solve problems, including problems involving three dimensions

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