The missing coordinates are listed below:
- (x₁, y₁) = (0, 1)
- (x₂, y₂) = (- √2 /2, √2 /2)
- (x₃, y₃) = (- 1, 0)
- (x₄, y₄) = (- √2 /2, - √2 /2)
- (x₅, y₅) = (0, - 1)
- (x₆, y₆) = (- √2 /2, √2 /2)
- (x₇, y₇) = (1, 0)
How to determine the location a terminal point in a unit circle
According to the polar coordinate system, a vector in standard position is defined by this parametric formula:
(x, y) = (r · cos t, r · sin t), where t is in radians.
If we assume that r = 1, then we proceed to determine the location of the seven points remaining:
(x₁, y₁) = (cos π/2, sin π/2)
(x₁, y₁) = (0, 1)
(x₂, y₂) = (cos 3π/4, sin 3π/4)
(x₂, y₂) = (- √2 /2, √2 /2)
(x₃, y₃) = (cos π, sin π)
(x₃, y₃) = (- 1, 0)
(x₄, y₄) = (cos 5π/4, sin 5π/4)
(x₄, y₄) = (- √2 /2, - √2 /2)
(x₅, y₅) = (cos 3π/2, sin 3π/2)
(x₅, y₅) = (0, - 1)
(x₆, y₆) = (cos 7π/4, sin 7π/4)
(x₆, y₆) = (- √2 /2, √2 /2)
(x₇, y₇) = (cos 2π, sin 2π)
(x₇, y₇) = (1, 0)
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