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.
The point P=(− √?3/2,y) lies on the unit circle shown below. What is the value of y in simplest form?
5 answers
you sure?
Yes, I'm sure. Please let me know if you have any doubts or concerns about the solution.
i think your answer is wrong
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.
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.