Find a calculator approximation to four decimal places for each circular function value. See Example 3.
sec 2.8440

Verified step by step guidance

1. Understand that secant (sec) is the reciprocal of cosine, so \( \sec \theta = \frac{1}{\cos \theta} \).
2. Identify the angle given in the problem, which is \( \theta = 2.8440 \) radians.
3. Use a calculator to find \( \cos(2.8440) \).
4. Calculate the reciprocal of the cosine value obtained: \( \sec(2.8440) = \frac{1}{\cos(2.8440)} \).
5. Round the result to four decimal places to get the final approximation.

Key Concepts

Circular Functions

Circular functions, also known as trigonometric functions, relate the angles of a circle to the ratios of its sides. The primary circular functions include sine, cosine, tangent, and their reciprocals: cosecant, secant, and cotangent. Understanding these functions is essential for evaluating angles and their corresponding values in various contexts, such as in the given problem.

Secant Function

The secant function is defined as the reciprocal of the cosine function. Mathematically, sec(θ) = 1/cos(θ). It is important to know how to compute the secant of an angle, especially when using a calculator, as it directly relates to the cosine value of that angle. In this case, finding sec(2.8440) requires calculating the cosine first.

Calculator Approximations

Calculator approximations involve using a scientific calculator to find numerical values of trigonometric functions to a specified degree of accuracy, such as four decimal places. This process typically includes entering the angle in radians or degrees and selecting the appropriate function. Understanding how to read and interpret these approximations is crucial for solving problems that require precise values.