Question

Determine the equation of this sine function.Two trigonometric functions are graphed. One has a lot more "bumps" in the same space than the other, but it's no taller. What could the equation be?

Answer 1

Answer::

$y=sin(3x)$

Explanation:

The general form of a sine function is given as:

$\begin{gathered} y=A\sin(Bx+C)+D \\ where \\ T=\frac{2\pi}{B} \end{gathered}$

As can be seen, the coefficient, B and the period, T of the sine curve has an inverse relationship.

Thus, as B gets bigger, the period becomes smaller and hence we have more bumps but the two functions still have the same height.

As an example, consider the functions below:

$\begin{gathered} y=\sin x \\ y=sin(3x) \end{gathered}$

The graphs are given below:

Observe that when B was increased to 3, the number of bumps increased as seen in the red graph.

Thus, the equation could be:

$y=sin(3x)$