π/6 (√3/2, 1/2)
x = r cos θ
The given point (π/6, (√3/2, 1/2)) is in polar coordinates, which means that we need to convert it into rectangular coordinates to better understand its location in the plane.
To convert from polar to rectangular coordinates, we use the following formulas:
x = r cos θ
y = r sin θ
where r is the distance from the origin to the point, θ is the angle formed by the line segment connecting the origin and the point and the positive x-axis, and (x, y) are the Cartesian coordinates of the point.
In this case, we have:
r = 1 (since the point is one unit away from the origin)
θ = π/6 (since the angle formed by the line segment connecting the origin and the point and the positive x-axis is π/6)
We can now use the formulas to find the rectangular coordinates:
x = r cos θ = 1 cos(π/6) = √3/2
y = r sin θ = 1 sin(π/6) = 1/2
So the rectangular coordinates of the point in question are (√3/2, 1/2).
To summarize, the point (π/6, (√3/2, 1/2)) in polar coordinates can be converted into rectangular coordinates using the formulas x = r cos θ and y = r sin θ, where r is the distance from the origin to the point and θ is the angle formed by the line segment connecting the origin and the point and the positive x-axis. The rectangular coordinates of the point are (√3/2, 1/2).
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