Trigonometric Functions Question 5

A cosine function is shown in the standard $(x,y)$ coordinate plane below.

One of the following equations represents this function. Which one?

y= 2\cos{\left(\dfrac{x}{3}\right)}

y=2\cos{(3x)}

y= 3\cos{\left(\dfrac{x}{3}\right)}

y= 3\cos{\left(\dfrac{x}{2}\right)}

y=3\cos{(2x)}

Approach

The amplitude is $3$ . The period is $\pi$ .

The standard equation for a trigonometric function is:

y=A\cos{B(x-C)}+D

The amplitude is $A$ and the period is related to $B$ by:

\text{Period} = \frac{2\pi}{B}

B = \frac{2\pi}{\text{Period}}

B = \frac{2\pi}{\pi} = 2