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.
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)
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!!
3 answers
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.
If the line makes an angle θ with the +x axis, then it makes an angle θ/2 - θ with the -y axis.
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°
it would be
θ + π/2 = appr 2.034 radians or appr 116.57°