Question

The point P=(− √?3/2,y) lies on the unit circle shown below. What is the value of y in simplest form?

Answer 1

[AI-generated answer — Bot]

Since P lies on the unit circle, we know that its distance from the origin is 1. This gives us the equation:

√((-√3/2)^2 + y^2) = 1

Simplifying:

√(3/4 + y^2) = 1

Square both sides:

3/4 + y^2 = 1

y^2 = 1/4

y = ±1/2

Since P is in the second quadrant (its x-coordinate is negative), we choose the negative square root:

y = -1/2

Therefore, the value of y in simplest form is -1/2.

Answer 2

you sure?

Answer 3

[AI-generated answer — Bot]

Yes, I'm sure. Please let me know if you have any doubts or concerns about the solution.

Answer 4

i think your answer is wrong

Answer 5

[AI-generated answer — Bot]

I apologize if my previous answer was incorrect. Please allow me to check my work and provide a corrected solution.

If P is given by the coordinate (-√3/2, y) on the unit circle, we know that the sum of the squares of its coordinates is equal to 1:

(-√3/2)^2 + y^2 = 1

3/4 + y^2 = 1

y^2 = 1 - 3/4

y^2 = 1/4

y = ±√1/4 = ±1/2

Since P lies in the second quadrant, its y-coordinate is negative. Therefore, y = -1/2 is the correct value in simplest form.

So, the value of y in simplest form is -1/2.

Answer 6

[AI-generated answer — Step-by-Step Bot]

To find the value of y in simplest form, we can use the equation of a unit circle, which is x^2 + y^2 = 1. Since the point P lies on the unit circle, the coordinates of P satisfy this equation.

Given that the x-coordinate of P is -√3/2, we can substitute this value into the equation to solve for y:

(-√3/2)^2 + y^2 = 1
3/4 + y^2 = 1
y^2 = 1 - 3/4
y^2 = 1/4

To find the value of y, we take the square root of both sides:

√(y^2) = √(1/4)
y = ±1/2

Therefore, the value of y in simplest form is ±1/2.

Answer 7

[AI-generated answer — Explain Bot]

To find the value of y, we need to use the equation of the unit circle: x^2 + y^2 = 1.

In this case, we are given that x = -√3/2. Plugging this into the equation, we have:

(-√3/2)^2 + y^2 = 1

Simplifying, we get:

3/4 + y^2 = 1

Subtracting 3/4 from both sides, we get:

y^2 = 1 - 3/4

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

To find the value of y, we take the square root of both sides:

y = ±√(1/4)

Since we're looking for the value of y in simplest form, we can simplify the square root:

y = ±(1/2)

Therefore, the value of y in simplest form is y = ±(1/2).