if the terminal ray of an angle 0 in standard position passes through the point (-1,3),then cos0=
the hypotenuse is sqrt(10)
cosx = -1/sqrt(10) = -.316
x = 108.43 degrees
To find the value of cos(θ) when the terminal ray of an angle θ in standard position passes through a given point (-1, 3), we need to determine the values of the adjacent side and the hypotenuse of the right triangle formed by the angle and the given point.
In standard position, the angle θ is formed between the positive x-axis and the terminal ray of the angle. Since the terminal ray of the angle passes through the point (-1, 3), we can consider the horizontal distance from the origin (0, 0) to the given point (-1, 3) as the adjacent side and the distance from the origin to the given point as the hypotenuse.
Using the Pythagorean theorem, we can calculate the values of the adjacent side and the hypotenuse:
Adjacent side (a) = x-coordinate of the given point = -1
Hypotenuse (h) = distance from origin to the given point = sqrt((-1)^2 + 3^2) = sqrt(1 + 9) = sqrt(10)
Now, we can calculate the value of cos(θ) using the formula:
cos(θ) = adjacent side / hypotenuse = a / h = -1 / sqrt(10)
Therefore, cos(θ) = -1 / sqrt(10).