Question

The point (x, square root of 3/2) is on the unit circle, what is x?

Answer 1

Answer: x = 1/2

Explanation:

We have that the point (x, (√3)/2)) is on the unit circle.

we can define a circle of radius R centered in the (0,0) as:

x^2 + y^2 = R^2

This means that:

x^2 + (√(3)/2)^2 = 1

x^2 + 3/4 = 1

x^2 = 1 - 3/4 = 1/4

x = √(1/4) = 1/2

So we have that x is equal to 1/2

Answer 2

`x=(1)/(2)`

Explanation:

When we have a point (a,b) on the unit circle, we can say that

`a^2+b^2=1`

This is a property of the unit circle.

From the point given
`(x,(√(3) )/(2))` , now we can write the equation shown below and solve for x:

`x^2+((√(3) )/(2))^2=1\\x^2+(3)/(4)=1\\x^2=1-(3)/(4)\\x^2=(1)/(4)\\x=(√(1))/(√(4) ) \\x=(1)/(2)`

So, x = 1/2