Secant of an angle in a right triangle is defined as which ratio?

Secant of an angle in a right triangle is defined as which ratio?

• A. Hypotenuse over adjacent
• B. Opposite over adjacent
• C. Adjacent over opposite
• D. Hypotenuse over opposite

Answer: (A)

Secant of an angle in a right triangle is the ratio of the hypotenuse to the adjacent side. This comes from the cosine definition: cos theta = adjacent/hypotenuse, so sec theta = 1/cos theta = hypotenuse/adjacent. In a right triangle, the hypotenuse is the side opposite the right angle, and the adjacent side is the leg that touches the angle in question. For context, tangent is opposite over adjacent, cotangent is adjacent over opposite, and cosecant is hypotenuse over opposite. So the secant ratio directly corresponds to hypotenuse over adjacent.

Secant of an angle in a right triangle is the ratio of the hypotenuse to the adjacent side. This comes from the cosine definition: cos theta = adjacent/hypotenuse, so sec theta = 1/cos theta = hypotenuse/adjacent. In a right triangle, the hypotenuse is the side opposite the right angle, and the adjacent side is the leg that touches the angle in question.

For context, tangent is opposite over adjacent, cotangent is adjacent over opposite, and cosecant is hypotenuse over opposite. So the secant ratio directly corresponds to hypotenuse over adjacent.