Question

In a unit circle, θ = 360°. What is the terminal point?

a) (0, -1)
b) (0, 1)
c) (-1, 0)
d) (1, 0)

Answer 1

In a unit circle, the terminal point for θ = 360° is where the radial line completes a full rotation and intersects the unit circle at its starting point, which has coordinates (1, 0).

Step-by-step explanation:

In a unit circle, when θ = 360°, the angle has completed a full rotation around the circle. In terms of radians, this is equivalent to 2π radians, as 360° is the angle for a full circle. The terminal point is located where the radial line intersects the unit circle, which in the case of a full rotation, ends up back at the starting point on the circumference.

For any angle θ on a unit circle, the terminal point can be found at coordinates (cosθ, sinθ). Since cos 360° = 1 and sin 360° = 0, the terminal point at θ = 360° is found to be at the coordinates (1, 0). Therefore, the correct answer is (d) (1, 0).