Question

On the unit circle, which of the following angles has the terminal point coordinates ( -v2/2 , -v2/2)

Answer 1

The terminal point coordinates (-√2/2, -√2/2) indicate an angle of 225° on the unit circle since it is the position in the third quadrant with both negative x and y components.

Step-by-step explanation:

On the unit circle, if we have the terminal point coordinates (-√2/2, -√2/2), we are dealing with an angle that is located in the third quadrant. In the unit circle, all coordinates are of the form (√2/2, √2/2), (√2/2, -√2/2), (-√2/2, √2/2), or (-√2/2, -√2/2) for the angles 45°, 315° (or -45°), 135°, and 225° respectively. Therefore, the answer is 225°, since this is the angle in the third quadrant with negative values for both the x and y coordinates on the unit circle.

Answer 2

Step-by-step explanation:

A unit circle means radius of the circle = 1 unit

Let a terminal point on the circle is (x, y) and angle between the point P and x-axis is θ.

Center of the circle is origin (0, 0).

Therefore, ordered pair representing the terminal point will be (OP×Cosθ, OP×Sinθ) =

OP.Cosθ = 1×Cosθ =

Cosθ =

θ = , where n = integers

Similarly, OP×Sinθ = 1×Sinθ = -

Sinθ = -

θ = , where n = integer

Common value of θ will be, θ =

Option B will be the answer.