Question

Which graph represents the trigonometric function given below?

Answer 1

The last graph is your answer.

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 - (\pi)/(3) ) - 1 = 0`

`2 \cos(2x - (\pi)/(3) ) = 1`

`\cos(2x - (\pi)/(3) ) = (1)/(2)`

Take the inverse cosine of both sides

`2x - (\pi)/(3) = \cos {}^( - 1) ( (1)/(2) )`

`2x - (\pi)/(3) = (\pi)/(3) + 2\pi(n)`

Or

`2x - (\pi)/(3) = (5\pi)/(3) + 2\pi(n)`

Solve for x. in both scenarios

`x = (\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.