Question

Which angle, θ, forms the point on the unit circle with the coordinates (sqrt2/2, sqrt2/2)?

30
45
60
90

Answer 1

If you look at a unit circle (or you have one memorized, which I would strongly suggest) (√2/2,√2/2) is located at the radian value
`\pi /4`, which is 45 degrees

Answer 2

Option B.

Explanation:

The given point is

`((√(2))/(2),(√(2))/(2))`

Both coordinates are positive, so the point lies in the 1st quadrant.

We need to find the angle, θ, forms the point on the unit circle with the given point.

If a point is (a,b), then

`\tan \theta=(b)/(a)`

Using this formula we get

`\tan \theta=((√(2))/(2))/((√(2))/(2))`

`\tan \theta=1`

`\tan \theta=\tan (45^(\circ))`

On comparing boh sides we get

`\theta=45^(\circ)`

Therefore, the correct option is B.