When pi/2<theta<3pi/4, which of the following could possibly be tan theta.

a. -8
b. -1/8
c. 0
d. 1/8
e. 8

in the second quadrant, tan is negative, and in the third quadrant, tan is positive. What is tan PI?

a. -8

If you look at a graph of y = tan theta, you will see why.

Table:

Theta......tan theta
....0...............0.......
..pi/4.............1.......
->pi/2-......->+inf...
->pi/2+......->-inf....
.3pi/4............-1......
....pi...............0......

And so on.

Max is right, I read 3/4 PI as 270 degrees, which it is not.

http://intmstat.com/trigonometric-graphs/cotx.gif

To determine which of the given options could possibly be the tangent of theta when pi/2 < theta < 3pi/4, we need to understand the properties of the tangent function within this interval.

The tangent function (tanθ) can be defined as the ratio of the sine (sinθ) to the cosine (cosθ) of an angle. In this case, we need to determine which values of the tangent function lie within the interval (pi/2, 3pi/4).

For a given theta, if the value of tan(theta) is positive, it means that both sin(theta) and cos(theta) have the same sign (+ or -). If the value of tan(theta) is negative, it means that sin(theta) and cos(theta) have opposite signs.

Now, let's analyze each option:

a. -8: This value is negative, so it could potentially be the tangent of a theta value between pi/2 and 3pi/4. Therefore, it is a valid option.

b. -1/8: Similarly, this value is negative, so it could also be the tangent of a theta value within the given range. Therefore, it is a valid option.

c. 0: The tangent of an angle is zero only if the angle itself is an integer multiple of pi. Since pi/2 < theta < 3pi/4, which is not an integer multiple of pi, this option is not valid.

d. 1/8: This value is positive, so it cannot be the tangent of a theta value between pi/2 and 3pi/4. Therefore, it is not a valid option.

e. 8: Similarly, this value is positive, so it cannot be the tangent of a theta value within the given range. Therefore, it is not a valid option.

In conclusion, options a. (-8) and b. (-1/8) could possibly be the tangent of a theta value when pi/2 < theta < 3pi/4.