Question

which of the following explains why $\cos 60^\circ = \sin 30^\circ$ using the unit circle?
\bigcirc\\; the side opposite a $30^\circ$ angle is the same as the side adjacent to a $60^\circ$ angle in a right triangle. on a unit circle, the $y$ (sin) distance of a $30^\circ$ angle is the same as the $x$ (cos) distance of a $60^\circ$ angle.
\bigcirc\\; the side opposite a $30^\circ$ angle is the same as the side adjacent to a $60^\circ$ angle in a right triangle. on a unit circle, the $x$ (sin) distance of a $30^\circ$ angle is the same as the $y$ (cos) distance of a $60^\circ$ angle.
\bigcirc\\; the ratios describe different sides of the same right triangle. on a unit circle, the $y$ (sin) distance of a $30^\circ$ angle is the same as the $x$ (cos) distance of a $60^\circ$ angle.
\bigcirc\\; the ratios describe different sides of the same right triangle. on a unit circle, the $x$ (sin) distance of a $30^\circ$ angle is the same as the $y$ (cos) distance of a $60^\circ$ angle.

Explanation:

In a right triangle with angles 30° and 60°, the side opposite 30° equals the side adjacent to 60°. On the unit circle, sinθ = y-coordinate and cosθ = x-coordinate. Thus, sin30° (y of 30°) equals cos60° (x of 60°). The first option correctly links the triangle side relationship to unit circle coordinates.

Answer:

A. The side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the y (sin) distance of a 30° angle is the same as the x (cos) distance of a 60° angle.