the terminal side of an angle in standard position coincides with the line x-2y=0, what is the cosine to the nearest ten-thousandth??? I am completely lost with this one
x-2y = 0.
2y = x.
y = (1/2)x.
Slope = 1/2 = Tan A.
A = 26.57o.
Cos 26.57 = 0.89443.
No problem, I can help you solve this problem step by step.
To find the cosine of an angle, we need to determine the x and y coordinates of a point on the terminal side of the angle. In this case, we know that the terminal side of the angle coincides with the line x - 2y = 0.
To find the x and y coordinates, we can set y to any arbitrary value and solve for x. Let's choose y = 0 for simplicity:
x - 2(0) = 0
x = 0
So, one point on the line is (0, 0).
Next, we draw a right triangle using this point on the x-axis (0, 0) and the origin (0, 0). The hypotenuse of the triangle will be the distance between the origin and the point on the line.
Now, we can calculate the length of the hypotenuse using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, (x1, y1) = (0, 0) and (x2, y2) is the point on the line we found earlier.
d = sqrt((0 - 0)^2 + (0 - 0)^2)
d = sqrt(0 + 0)
d = sqrt(0)
d = 0
Since the length of the hypotenuse is 0, we can conclude that the angle is a 0-degree angle.
Finally, the cosine of a 0-degree angle is equal to 1.
Therefore, the cosine of the angle (nearest ten-thousandth) is 1.