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.
Fill in the gaps below.
A rotation of $390^\circ$390° has the same rotation as the acute angle with measure $\editable{}$$^{\circ}$∘.
So $\sin390^\circ$sin390°$=$=$\sin\editable{}$sin.
A rotation of $480^\circ$480° has the same rotation as the obtuse angle with measure $\editable{}$$^{\circ}$∘.
So $\sin480^\circ$sin480°$=$=$\sin\editable{}$sin.
A rotation of $570^\circ$570° has the same rotation as the reflex angle with measure $\editable{}$$^{\circ}$∘.
So $\sin570^\circ=\sin210^\circ$sin570°=sin210°.
Here is the graph of $y=\sin\theta$y=sinθ for $0\le\theta\le720^\circ$0≤θ≤720°.
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.
The function values and shape of the graph repeat at irregular intervals.
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.
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.