Building blocks

# Sine stretching Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Solution

Use the slider to change the value of $a$.

• What do you notice?
• What questions do you have?

Decide which of the following is the gradient function of $\sin 3x$ and justify your answer.

1. $\cos 3x$
2. $3\cos x$
3. $3\cos 3x$

Two possible ways to decide which is the gradient function are explored below.

After thinking about the different ways you could have got the answer, can you see the two effects that the value of $a$ has in the applet below?

For any value of $a$, what is the gradient function of $\sin ax$ (assuming $a \neq 0$)?