Secant

Definition

A secant is a line that intersects a circle at two distinct points. It is one of the fundamental trigonometric functions, along with sine, cosine, tangent, and others, that describe the relationships between the sides and angles of a right triangle.

5 Must Know Facts For Your Next Test

1. The secant function, denoted as sec(x), is the reciprocal of the cosine function, meaning sec(x) = 1/cos(x).
2. Secant lines are used to find the slope of a curve at a specific point, which is important in calculus for finding derivatives.
3. The secant function is periodic, with a period of $2\pi$, meaning sec(x + $2\pi$) = sec(x).
4. The domain of the secant function is all real numbers except for odd multiples of $\pi/2$, where the cosine function is zero, and the secant function is undefined.
5. The secant function is often used in trigonometric identities and equations, such as the Pythagorean identity: $\sec^2(x) = 1 + \tan^2(x)$.

Review Questions

• Explain how the secant function is related to the right triangle trigonometry discussed in Section 7.2.
  • In the context of right triangle trigonometry, the secant function is one of the fundamental trigonometric functions that describe the relationships between the sides and angles of a right triangle. Specifically, the secant function is the reciprocal of the cosine function, meaning it represents the ratio of the hypotenuse to the adjacent side of a right triangle. Understanding the secant function and its properties is crucial for solving problems involving right triangle trigonometry, such as finding missing side lengths or angle measures.
• Describe how the secant function is used in the graphs of the other trigonometric functions discussed in Section 8.2.
  • The secant function, along with the other trigonometric functions, plays a key role in the graphs of the trigonometric functions discussed in Section 8.2. The secant function has a periodic graph, with a period of $2\pi$, and its graph is the reciprocal of the cosine function's graph. Understanding the characteristics of the secant function's graph, such as its domain, range, and behavior near asymptotes, is essential for analyzing and interpreting the graphs of the other trigonometric functions and their relationships.
• Explain how the secant function is used in the process of verifying trigonometric identities and simplifying trigonometric expressions, as discussed in Section 9.1.
  • The secant function is often used in the process of verifying trigonometric identities and simplifying trigonometric expressions, as discussed in Section 9.1. This is because the secant function is related to other trigonometric functions through various identities, such as the Pythagorean identity $\sec^2(x) = 1 + \tan^2(x)$. By understanding the properties and relationships of the secant function, you can manipulate and transform trigonometric expressions, ultimately simplifying them or verifying the validity of trigonometric identities.

Related terms

Trigonometric Functions: Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. The primary trigonometric functions are sine, cosine, and tangent.

Right Triangle: A right triangle is a triangle in which one of the angles is a 90-degree angle, or a right angle. The sides of a right triangle are often labeled as the hypotenuse, adjacent, and opposite.

Inverse Trigonometric Functions: Inverse trigonometric functions, also known as arcsin, arccos, and arctan, are used to find the angle given the value of a trigonometric function.