Question

Write a correct equation for the function whose graph is shown.

Answer 1

y=-2sin6x

Explanation:

Answer 2

`\displaystyle y=-2sin(6t)`

Explanation:

Sinusoid

The shape of a sinusoid is well-know because it describes a curve with a smooth and periodic oscillation. The sine and cosine are the two trigonometric functions in which the graph matches the description of a sinusoid. The sine can be identified because its value is zero at time zero.

The graph shown in the figure corresponds to a sine. The other characteristics of the sine function are

* It completes a cycle in
`2\pi` radians

* It has a maximum of 1 and a minimum of -1

* It's increasing for a quarter of the cycle, decreasing for half of the cycle, and increasing for the remaining quarter of the cycle

* The equation is

`y=Asin(wt)`

The function starts decreasing for the first quarter, which only is possible if the amplitude A is negative. We can also see the maximum and minimum values are 2 and -2 respectively. This means the amplitude is A=-2

We can also see the function completes 3 cycles in
`t=\pi` radians or 6 cycles in
`2\pi` radians. Or, equivalently

`wt=12\pi`

`w(2\pi)=12\pi`

`\displaystyle w=(12)/(2)=6\ rad/sec`

Thus, the function can be expressed as

`\boxed{\displaystyle y=-2sin(6t)}`