Find the cos(Θ) of an angle in standard position if the terminal side passes through the point (4, -8).

-2
-2/sqrt5
1/sqrt5
2

I think it is C but I am not so sure.

C is correct

To find the cosine of an angle in standard position given the point (4, -8), we need to determine the length of the adjacent side and the hypotenuse.

The length of the adjacent side is the x-coordinate of the point, which is 4. The length of the hypotenuse can be found using the Pythagorean theorem:

hypotenuse² = adjacent side² + opposite side²
hypotenuse² = 4² + (-8)²
hypotenuse² = 16 + 64
hypotenuse² = 80

Taking the square root of both sides, we have:
hypotenuse = √80 = 4√5

Now, we can find the cosine of the angle:
cos(Θ) = adjacent side / hypotenuse
cos(Θ) = 4 / 4√5 = 1/√5

So the correct answer is C) 1/√5.

To find the value of cos(Θ) for an angle in standard position, when the terminal side passes through a specific point, you can use the coordinates of that point.

In this case, the point given is (4,-8). To determine Θ, we can use the right triangle formed by the point (4,-8) and the origin (0,0) as one vertex.

The length of the horizontal leg is 4, and the length of the vertical leg is -8 (negative because the point is below the x-axis). We can now use these lengths to find the value of cos(Θ) using the cosine definition:

cos(Θ) = adjacent/hypotenuse

In this case, the adjacent side is the horizontal leg (4) and the hypotenuse is the distance from the origin (0,0) to the point (4,-8), which can be found using the Pythagorean theorem:

hypotenuse = sqrt((4^2) + (-8^2))
hypotenuse = sqrt(16 + 64)
hypotenuse = sqrt(80)
hypotenuse = 4√5

Now we can substitute these values into the cosine definition:

cos(Θ) = 4/4√5

To simplify this expression, we can multiply both the numerator and denominator by √5:

cos(Θ) = (4/4√5) * (√5/√5)
cos(Θ) = (4√5)/(4 * 5)
cos(Θ) = (4√5)/20
cos(Θ) = √5/5

Therefore, the answer is option C) 1/√5 or √5/5.