In a right triangle, cosecant is defined as which ratio?

In a right triangle, cosecant is defined as which ratio?

• A. hypotenuse/opposite
• B. opposite/hypotenuse
• C. adjacent/opposite
• D. adjacent/hypotenuse

Answer: (A)

Cosecant is the reciprocal of sine, so in a right triangle it is the ratio of the hypotenuse to the side opposite the angle. In other words, it tells you how many times the opposite side would fit into the hypotenuse, not the other way around. This is why the correct expression is hypotenuse divided by opposite. For example, if the opposite side is 3 units and the hypotenuse is 5 units, sine would be 3/5, while cosecant would be 5/3. The other basic functions are cosine, which is adjacent over hypotenuse, and tangent, which is opposite over adjacent, so they don't describe the cosecant.

Cosecant is the reciprocal of sine, so in a right triangle it is the ratio of the hypotenuse to the side opposite the angle. In other words, it tells you how many times the opposite side would fit into the hypotenuse, not the other way around. This is why the correct expression is hypotenuse divided by opposite.

For example, if the opposite side is 3 units and the hypotenuse is 5 units, sine would be 3/5, while cosecant would be 5/3. The other basic functions are cosine, which is adjacent over hypotenuse, and tangent, which is opposite over adjacent, so they don't describe the cosecant.