Which of the following ratios correctly describes the tangent function?

Check the final answer first, then review the worked steps.

Problem

Which of the following ratios correctly describes the tangent function?

Answer

\(B. \frac{opp}{adj}\)

Step-by-step solution

  1. Understand Trigonometric Ratios: In a right-angled triangle, trigonometric functions relate the angles to the ratios of the lengths of its sides. The three primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan).

2. Recall the Definitions:
- Sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse: $\sin(\theta) = \frac{opposite}{hypotenuse}$
- Cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse: $\cos(\theta) = \frac{adjacent}{hypotenuse}$
- Tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle: $\tan(\theta) = \frac{opposite}{adjacent}$

3. Evaluate the Options:
- Option A: $\frac{adjacent}{hypotenuse}$ describes the cosine function.
- Option B: $\frac{opposite}{adjacent}$ describes the tangent function.
- Option C: $\frac{opposite}{hypotenuse}$ describes the sine function.

  1. Identify the Correct Ratio: Based on the definitions, the ratio that correctly describes the tangent function is $\frac{opposite}{adjacent}$.