In a right-angled triangle, the ratio of the adjacent side to the hypotenuse defines which trigonometric function?

In a right-angled triangle, the ratio of the adjacent side to the hypotenuse defines which trigonometric function?

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

Answer: (B)

In a right-angled triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. This means you compare the leg that touches the angle with the longest side opposite the right angle. This is different from sine, which uses the opposite side, and from tangent, which uses the opposite over the adjacent, or cosecant, which is the reciprocal of sine (hypotenuse over opposite). A helpful check: as the angle grows toward 90 degrees, the adjacent side gets smaller relative to the hypotenuse, so cosine decreases toward zero; when the angle is very small, the adjacent side is close in length to the hypotenuse, so cosine is near one. So the ratio of adjacent to hypotenuse is cosine.

In a right-angled triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. This means you compare the leg that touches the angle with the longest side opposite the right angle. This is different from sine, which uses the opposite side, and from tangent, which uses the opposite over the adjacent, or cosecant, which is the reciprocal of sine (hypotenuse over opposite). A helpful check: as the angle grows toward 90 degrees, the adjacent side gets smaller relative to the hypotenuse, so cosine decreases toward zero; when the angle is very small, the adjacent side is close in length to the hypotenuse, so cosine is near one. So the ratio of adjacent to hypotenuse is cosine.