Question

What is the value of the y-coordinate of point A?

Answer 1

-1/2

Explanation:

-1/2

Answer 2

The y-coordinate of point A is -
`\((1)/(2)\)`. Therefore, the value of the y-coordinate of point A is -0.5.

Given that the circle is centered at the origin (0, 0) and passes through the points (1, 0) and (-1, 0) on the x-axis, it is clear that the radius of the circle is 1.

Now, point A forms a 30-degree angle from the positive x-axis and is located in the third quadrant (negative y-axis). Since the radius is 1, the coordinates of point A can be represented as (-cos(30°), -sin(30°)).

Using the trigonometric values for a 30-degree angle:

`\[ \cos(30^\circ) = (√(3))/(2) \]`

`\[ \sin(30^\circ) = -(1)/(2) \]`

So, the coordinates of point A are
`\((- (√(3))/(2), -(1)/(2))\).`

The y-coordinate of point A is -
`\((1)/(2)\)`. Therefore, the value of the y-coordinate of point A is -0.5.