The point $P(-4,9)$ lies on the terminal arm of an angle $\theta$ in standard position.
Determine the exact value of $\cos (\theta)$, then enter the approximate value rounded to 4 decimal places.

Step 1 ：Given point P(-4, 9), we need to find the exact value of cos(θ) using the formula cos(θ) = x / r, where r is the distance from the origin to the point P.

Step 2 ：First, we need to find the distance r from the origin to the point P using the Pythagorean theorem: \(r = \sqrt{x^2 + y^2}\).

Step 3 ：\(x = -4\), \(y = 9\)

Step 4 ：\(r = \sqrt{(-4)^2 + (9)^2} = \sqrt{16 + 81} = \sqrt{97}\)

Step 5 ：Now that we have the value of r, we can find the exact value of cos(θ) using the formula cos(θ) = x / r.

Step 6 ：\(cos(θ) = \frac{-4}{\sqrt{97}}\)

Step 7 ：\(\boxed{cos(θ) = -\frac{4}{\sqrt{97}}}\)

Step 8 ：The approximate value of cos(θ) rounded to 4 decimal places is -0.4061.