Trigonometric Graphs

NZ Level 7 (NZC) Level 2 (NCEA)

Key features of sine and cosine curves

The value of $\sin\theta$`s``i``n``θ` can be represented on the $xy$`x``y`-plane below. Consider the curve $y=\sin\theta$`y`=`s``i``n``θ` 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 $\sin390^\circ$`s``i``n`390°$=$=$\sin\editable{}$`s``i``n`.

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

So $\sin480^\circ$`s``i``n`480°$=$=$\sin\editable{}$`s``i``n`.

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

So $\sin570^\circ=\sin210^\circ$`s``i``n`570°=`s``i``n`210°.

b

Here is the graph of $y=\sin\theta$`y`=`s``i``n``θ` for $0\le\theta\le720^\circ$0≤`θ`≤720°.

Loading Graph...

What do you notice about the nature of $y=\sin\theta$`y`=`s``i``n``θ`?

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`=`s``i``n``θ`.

Easy

Approx 3 minutes

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