Question

Which graph represents the trigonometric function given below?

Answer 1

Answer:

The last graph is your answer.

Step-by-step explanation:

The midline of the function should be in between the highest and lowest y value.

Here's the midline should be at y=-1

Let find where our zeroes occur at

$2 \cos(2x - \frac{\pi}{3} ) - 1 = 0$

$2 \cos(2x - \frac{\pi}{3} ) = 1$

$\cos(2x - \frac{\pi}{3} ) = \frac{1}{2}$

Take the inverse cosine of both sides

$2x - \frac{\pi}{3} = \cos {}^{ - 1} ( \frac{1}{2} )$

$2x - \frac{\pi}{3} = \frac{\pi}{3} + 2\pi(n)$

Or

$2x - \frac{\pi}{3} = \frac{5\pi}{3} + 2\pi(n)$

Solve for x. in both scenarios

$x = \frac{\pi}{3} + \pi(n)$

$x = \pi + \pi(n)$

So our zeroes occur at pi/3, and pi, and every pi units. So we should have a period of pi, and zeroes at pi/3, pi

The last graph is your answer.