We can use the given point (-2, 4) to find the values of the trigonometric functions for the angle in standard position that has its terminal side passing through that point.
First, we can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the given point and the origin:
h = sqrt((-2)^2 + 4^2) = sqrt(20) = 2sqrt(5)
Next, we can use the coordinates of the given point to determine the values of the trigonometric functions:
sin(0) = y/h = 4/2sqrt(5) = 2sqrt(5)/5
cos(0) = x/h = -2/2sqrt(5) = -sqrt(5)/5
tan(0) = y/x = -2/4 = -1/2
csc(0) = h/y = 2sqrt(5)/4 = sqrt(5)/2
sec(0) = h/x = -2sqrt(5)/2 = -sqrt(5)
cot(0) = x/y = -4/2 = -2
Therefore, the six trigonometric functions of the angle in standard position that has its terminal side passing through the point (-2,4) are:
sin(0) = 2sqrt(5)/5
cos(0) = -sqrt(5)/5
tan(0) = -1/2
csc(0) = sqrt(5)/2
sec(0) = -sqrt(5)
cot(0) = -2