Question

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

Answer 1

Answer:

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

Step-by-step 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

$wt=12\pi$

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

$\displaystyle w=\frac{12}{2}=6\ rad/sec$

Thus, the function can be expressed as

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