Define the secant function in terms of a right triangle.

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In the context of a right triangle, the **secant function** (denoted as **sec**) relates one of the non-right angles to the lengths of specific sides of the triangle. Here's how it's defined:

### Definition:
**Secant of an angle** in a right triangle is the ratio of the length of the **hypotenuse** to the length of the **adjacent side** relative to that angle.

### Mathematically:
$$
\sec(\theta) = \frac{\text{Hypotenuse}}{\text{Adjacent Side}}
$$

### Components Explained:
- **Hypotenuse:** The longest side of the right triangle, opposite the right angle.
- **Adjacent Side:** The side that forms the given angle (other than the hypotenuse).

### Illustration:

Consider a right triangle with angle $$ \theta $$:

```
       |
       |\
       | \
       |  \
       |   \
       |    \  Hypotenuse
       |     \
       |θ     \
       |_______\
      Adjacent
```

- **Angle $$ \theta $$:** One of the non-right angles in the triangle.
- **Adjacent Side:** The side adjacent to angle $$ \theta $$ (not the hypotenuse).
- **Hypotenuse:** The side opposite the right angle.

### Example:

Suppose in a right triangle, the adjacent side to angle $$ \theta $$ is **3 units**, and the hypotenuse is **5 units**. Then:

$$
\sec(\theta) = \frac{5}{3} \approx 1.6667
$$

### Relationship to Other Trigonometric Functions:

- **Secant is the reciprocal of the cosine function:**
  $$
  \sec(\theta) = \frac{1}{\cos(\theta)}
  $$
  
  Since cosine is defined as the ratio of the adjacent side to the hypotenuse:
  $$
  \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}
  $$
  Taking the reciprocal gives the secant:
  $$
  \sec(\theta) = \frac{\text{Hypotenuse}}{\text{Adjacent}}
  $$

### Important Notes:
- The secant function is **undefined** for angles where the adjacent side is **zero**, which corresponds to angles where the cosine is zero (e.g., $$ 90^\circ $$ and $$ 270^\circ $$ in the unit circle).
- In a right triangle, $$ \sec(\theta) $$ will always be **greater than or equal to 1** or **less than or equal to -1**, depending on the angle, because the hypotenuse is always at least as long as the adjacent side.

By understanding the secant function in terms of the sides of a right triangle, you can easily relate it to geometric representations and solve various trigonometric problems involving right-angled triangles.
In a right triangle, the **secant** of an angle is the ratio of the hypotenuse to the adjacent side. So, $$ \sec(\theta) = \frac{\text{Hypotenuse}}{\text{Adjacent Side}} $$.

Define the secant function in terms of a right triangle.

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