SAT Question 10e059a6: Circles answer and explanation with Desmos solution

Choice D is correct. It’s given that the measure of angle $A$ is $\frac{\pi }{216}$ radians and the measure of angle $B$ is $36$ times the measure of angle $A$. Therefore, the measure of angle $B$ is $36(\frac{\pi }{216})$ radians, or $\frac{\pi }{6}$ radians. A trigonometric ratio can be found using the unit circle, or a circle with radius $1$ unit. For a unit circle centered at the origin in the xy-plane, the cosine of $\frac{\pi }{6}$ radians is the x-coordinate of the point resulting from traveling a distance of $\frac{\pi }{6}$ counterclockwise from the point $(1,0)$. This results in the point $(\frac{\sqrt{3}}{2},\frac{1}{2})$. Therefore, the value of $\cos B$ is $\frac{\sqrt{3}}{2}$.