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?

Question

a)

0.523 radians

b)

1.249 radians

c)

0.463 radians

d)

1.047 radians
Been stuck on this for a few days now and can't figure it out, any help would be greatly appreciated!!

Answer 1

To find the angle, we need to first find the slope of the line passing through the point (4, 2) and the origin.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

m = (y2 - y1)/(x2 - x1)

Using the coordinates of the given point (4, 2) and the origin (0, 0), we get:

m = (2 - 0)/(4 - 0) = 1/2

Now, we know the slope of the line passing through the point and the origin.

The angle made between this line and the negative y-axis can be found using the inverse tangent function:

tan θ = m

θ = tan^-1(m)

θ = tan^-1(1/2)

θ = 0.464 radians (approx)

Therefore, the answer is option c) 0.463 radians.

Answer 2

AAAaannndd the bot gets it wrong yet again!

If the line makes an angle θ with the +x axis, then it makes an angle θ/2 - θ with the -y axis.

Answer 3

It asked for the angle between the line in quad I and the negative y-axis, so
it would be

θ + π/2 = appr 2.034 radians or appr 116.57°