Question

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

Answer 1

Option B

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) =
`((√(2) )/(2),-(√(2) )/(2))`

OP.Cosθ = 1×Cosθ =
`(1)/(√(2))`

Cosθ =
`(1)/(√(2))`

θ =
`(\pi )/(4)+2\pi n`,
`(7\pi )/(4)+2\pi n` where n = integers

Similarly, OP×Sinθ = 1×Sinθ = -
`(1)/(√(2))`

Sinθ = -
`(1)/(√(2) )`

θ =
`(5\pi )/(4)+2\pi n`,
`(7\pi )/(4)+2\pi n` where n = integer

Common value of θ will be, θ =
`(7\pi )/(4)`

Option B will be the answer.