The Unit Circle — Quiz

Question 22 • Precalculus

Which of the following explains why cosine 60 degrees is equal to sine 30 degrees using the unit circle?

Answer

The side opposite a 30 degrees angle is the same as the side adjacent to a 60 degrees angle in a right triangle. On a unit circle, the x times sine distance of a 30 degrees angle is the same as the y times cosine distance of a 60 degrees angle.

The side opposite a 30 degrees angle is the same as the side adjacent to a 60 degrees angle in a right triangle. On a unit circle, the y times sine distance of a 30 degrees angle is the same as the x times cosine distance of a 60 degrees angle.

The ratios describe different sides of the same right triangle. On a unit circle, the x times sine distance of a 30 degrees angle is the same as the y times cosine distance of a 60 degrees angle.

The ratios describe different sides of the same right triangle. On a unit circle, the y times sine distance of a 30 degrees angle is the same as the x times cosine distance of a 60 degrees angle.

Explanation

In a right triangle with angles 30° and 60°, the side opposite 30° is also the side adjacent to 60°. Therefore, the sine ratio for 30° equals the cosine ratio for 60°. On the unit circle, sine is the y-coordinate and cosine is the x-coordinate, so the y-coordinate at 30° matches the x-coordinate at 60°; both are 1/2.

AI-written and checked against the verified answer.

More from this Course

Quiz

Quiz

Quiz