Find the exact values of the six trigonometric functions of theta if the terminal side of theta in standard position contains the given point:

1. (8, 4)
2. (4, 4√3)
3. (0, -4)
4. (6, 2)

To find the exact values of the six trigonometric functions of θ for the given points, we need to determine the values of sine, cosine, tangent, cosecant, secant, and cotangent.

Before calculating these values, we need to determine the angle θ by using the point's coordinates. We can find this angle by using the inverse trigonometric functions.

1. For point (8, 4):
The angle θ can be found using the arctan function: θ = arctan(4/8) ≈ 26.57 degrees.

Now, let's calculate the trigonometric functions:

- Sine (sin): sin(θ) = opposite/hypotenuse = 4/10 = 2/5
- Cosine (cos): cos(θ) = adjacent/hypotenuse = 8/10 = 4/5
- Tangent (tan): tan(θ) = opposite/adjacent = 4/8 = 1/2
- Cosecant (csc): csc(θ) = 1/sin(θ) = 1/(2/5) = 5/2
- Secant (sec): sec(θ) = 1/cos(θ) = 1/(4/5) = 5/4
- Cotangent (cot): cot(θ) = 1/tan(θ) = 1/(1/2) = 2

So the exact values of the six trigonometric functions for the first point are:
sin(θ) = 2/5, cos(θ) = 4/5, tan(θ) = 1/2, csc(θ) = 5/2, sec(θ) = 5/4, cot(θ) = 2.

You can follow the same steps to solve the remaining points.