If a point on the Cartesian plane lies at (4, 2), what is the angle made between the line containing the point and the origin, and the negative y-axis?

a) 1.249 radians

b) 0.463 radians

c) 0.523 radians

d) 1.047 radians

well first what is the angle of line above the x axis ?

tan theta = 2/4 = 1/2
so theta = 26.565 degrees above x axis
that means it is also 26.565 degrees below the negative x axis
we want angle from there to 90 degrees below the x axis
90 - 26.56 = 63.43 degrees to straight down
63.43 * pi/180 =

b would be to the negative X axis.

typo?

make a sketch, and mark the angle you want

slope of the line is 1/2
so the tangent of the angle = 1/2

set your calculator to radians, angle in standard position would be .4636...
then your angle = (π/2 - .4636) = 1.107 radians, I don't see that answer

To find the angle between the line containing the point (4, 2) and the origin, and the negative y-axis, we need to use trigonometry.

Step 1: Find the slope of the line between the point and the origin.
The slope of the line is given by the formula:
m = (y2 - y1) / (x2 - x1)
In this case, (x1, y1) = (0, 0) (origin) and (x2, y2) = (4, 2) (point).
So, the slope (m) = (2 - 0) / (4 - 0) = 2 / 4 = 1/2.

Step 2: Find the angle (θ) formed by the line and the positive x-axis.
The angle θ can be found using the arctan function:
θ = arctan(m)
Substituting the value of m, we get:
θ = arctan(1/2)

Step 3: Calculate the angle between the line and the negative y-axis.
The angle between the line and the negative y-axis is equal to 90 degrees minus θ.
Let's convert θ from radians to degrees:
θ_degrees = arctan(1/2) * (180 / π)

Step 4: Calculate the final answer in radians.
The angle between the line and the negative y-axis in radians can be found by converting θ_degrees back to radians:
θ_radians = θ_degrees * (π / 180)

Now let's calculate the answer:
θ_degrees = arctan(1/2) * (180 / π) ≈ 26.565 degrees
θ_radians = θ_degrees * (π / 180) ≈ 0.463 radians

So, the correct answer is:
b) 0.463 radians.

I suspect a typo, means negative X axis

When i searched this question on google, some of the answers were saying b, so i typed b

"anonymous" is edging toward being banned if s/he continues to randomly hand out answers.

Be aware.