What trigonometric function is defined as the ratio of the opposite side to the hypotenuse?

What trigonometric function is defined as the ratio of the opposite side to the hypotenuse?

• A. Sine
• B. Cosine
• C. Tangent
• D. Cosecant

Answer: (A)

In trigonometry, the sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. So for a given acute angle, sin(angle) = opposite / hypotenuse. This makes sine the function that captures how tall the opposite side is relative to the longest side of the triangle. To see how this differs from the others: cosine uses adjacent over hypotenuse, tangent uses opposite over adjacent, and cosecant is the reciprocal of sine (hypotenuse over opposite). The described ratio—the opposite side divided by the hypotenuse—matches sine exactly.

In trigonometry, the sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. So for a given acute angle, sin(angle) = opposite / hypotenuse. This makes sine the function that captures how tall the opposite side is relative to the longest side of the triangle.

To see how this differs from the others: cosine uses adjacent over hypotenuse, tangent uses opposite over adjacent, and cosecant is the reciprocal of sine (hypotenuse over opposite). The described ratio—the opposite side divided by the hypotenuse—matches sine exactly.