sat suite question viewer

Choice D is correct. It's given that the circle is a unit circle, which means the circle has a radius of $1$. It's also given that point $G$ is the center of the circle and has coordinates $(0,0)$ and that point $H$ lies on the circle and has coordinates $(-1,y)$. Since the radius of the circle is $1$, the value of $y$ must be $0$, as all other points with an x-coordinate of $-1$ are a distance greater than $1$ away from point $G$. Since $F$ and $H$ are points on the unit circle centered at $G$, let side $FG$ be the starting side of the angle and side $GH$ be the terminal side of the angle. Since side $FG$ is on the positive x-axis and side $GH$ is on the negative x-axis, side $FG$ is half of a rotation around the unit circle, or $\pi$ radians, away from side $GH$. Therefore, the positive measure of angle $FGH$, in radians, is equal to $\pi$ plus an integer multiple of $2\pi$. In other words, the positive measure of angle $FGH$, in radians, is an odd integer multiple of $\pi$. Of the given choices, only $25\pi$ is an odd integer multiple of $\pi$.

Choice A is incorrect. This could be the positive measure of an angle where the starting side is $FG$ and the terminal side contains the point $(0,-1)$, not $(-1,0)$.

Choice B is incorrect. This could be the positive measure of an angle where the starting side is $FG$ and the terminal side contains the point $(0,1)$, not $(-1,0)$.

Choice C is incorrect. This could be the positive measure of an angle where the starting side is $FG$ and the terminal side contains the point $(1,0)$, not $(-1,0)$.