Question

Given the unit circle what is the value for y

Answer 1

Given a unit circle where the coordinate is represented by (cosθ, sinθ)

If the x coordinate is 1/2, then cos(x) = 1/2

Also, cosθ = adjancet side / hypotenuse. Therefore:

Adjacents side = 1 and hypotenuse = 2.

Now, the y missing coordinate is given by sinθ.

Where, sinθ = opposite side/ hypotenuse.

Then, we need to find the opposite side using the Pythagorean theorem, which is given by:

`c^2=a^2+b^2`

Where:

c = hypotenuse

a= adjacent side

b= opposite side.

We need to solve for b, then:

`b=\sqrt[]{c^2-a^2}`

Replace the values:

`b=\sqrt[]{(2)^2-(1)^2}`