Question

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

Answer 1

Answer:

Option B

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) = $(\frac{\sqrt{2} }{2},-\frac{\sqrt{2} }{2})$

OP.Cosθ = 1×Cosθ = $\frac{1}{\sqrt{2}}$

Cosθ = $\frac{1}{\sqrt{2}}$

θ = $\frac{\pi }{4}+2\pi n$,  $\frac{7\pi }{4}+2\pi n$ where n = integers

Similarly, OP×Sinθ = 1×Sinθ = -$\frac{1}{\sqrt{2}}$

Sinθ = -$\frac{1}{\sqrt{2} }$

θ = $\frac{5\pi }{4}+2\pi n$,  $\frac{7\pi }{4}+2\pi n$ where n = integer

Common value of θ will be, θ = $\frac{7\pi }{4}$

Option B will be the answer.