Which of the following is true of the location of an angle, Theta, whose tangent value is - sqrt3/3?
Theta has a 30-degree reference angle and is located in Quadrant II or IV
Theta has a 30-degree reference angle and is located in Quadrant II or III
Theta has a 60-degree reference angle and is located in Quadrant II or IV
Theta has a 60-degree reference angle and is located in Quadrant II or III

Step-by-step explanation:

Keep in mind that the tangent function is negative in Quadrants II and IV.

Of the three possible answers, the 2nd is invalid because the tangent is positive in Q III.

If the reference angle were in Quadrant II and had the value 30° (second possible answer), then the opposite side would be +1, the adjacent side -√3 and the hypotenuse 2.  Based on this, the tangent of theta would be opp / adj, or +1 / (-√3)  or -√3/3.    This is correct.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.