Final answer:
Cosine of the angle θ with point N(-7, -1) on its terminal side is calculated using adjacent side over hypotenuse, resulting in cos θ being equal to -7 divided by √50, so the answer is -7/√50.
Step-by-step explanation:
If N(-7, -1) is a point on the terminal side of θ in standard position, we want to find the exact value of cos θ.
To find the cosine of an angle, we need to use the coordinates of point N. In the context of a right-angled triangle, cos θ is the adjacent side divided by the hypotenuse.
The adjacent side to angle θ here is -7 (the x-coordinate of point N), and the hypotenuse can be calculated using the Pythagorean theorem: the square root of (-7)2 + (-1)2, which equals √50. Therefore, cos θ is equal to -7 divided by √50, which simplifies to √2/10. So, cos θ = -7/√50.
Thus, the correct answer would be a) cos θ = -7/√50.